#Mac
knitr::opts_knit$set(root.dir = "~/Dropbox/R backup/SDCT - R")

#Windows
#knitr::opts_knit$set(root.dir = "C:/Users/rowe0122/Dropbox/R backup/SDCT - R")
library(knitr)

Load data

load(file="Baseline.Rdata")
load(file="SDCTCOW.Rdata")
load(file="SDCTCOWDHI.Rdata")

SDCTCOW = SDCTCOW %>%
  mutate(Tx = recode(SDCTCOW$Tx,
                     "0" = "Blanket", "1" = "Culture", "2" = "Algorithm"))

Import file BL (cows included for analysis) for descriptive statistics

library(readr)

Attaching package: ‘readr’

The following object is masked from ‘package:scales’:

    col_factor
BL <- read_csv("BL.csv", col_types = cols(X1 = col_skip()))
Missing column names filled in: 'X1' [1]
head(BL)

Inspect data

print(summarytools::dfSummary(BL, valid.col=FALSE, graph.magnif=0.8, style="grid"), method = "render")
NAs introduced by coercion

Data Frame Summary

BL

Dimensions: 1211 x 10
Duplicates: 0
No Variable Stats / Values Freqs (% of Valid) Graph Missing
1 Site [character] 1. CA 2. IA 3. MN 4. NY
630(52.0%)
263(21.7%)
160(13.2%)
158(13.1%)
0 (0%)
2 FARMID [numeric] Mean (sd) : 4 (1.5) min < med < max: 1 < 4 < 7 IQR (CV) : 2 (0.4)
1:76(6.3%)
2:82(6.8%)
3:263(21.7%)
4:388(32.0%)
5:242(20.0%)
6:47(3.9%)
7:113(9.3%)
0 (0%)
3 Tx [numeric] Mean (sd) : 1 (0.8) min < med < max: 0 < 1 < 2 IQR (CV) : 2 (0.8)
0:407(33.6%)
1:410(33.9%)
2:394(32.5%)
0 (0%)
4 Age [numeric] Mean (sd) : 47 (15.4) min < med < max: 30.4 < 44.5 < 122.3 IQR (CV) : 22.6 (0.3) 682 distinct values 0 (0%)
5 Parity [numeric] Mean (sd) : 1.9 (0.8) min < med < max: 1 < 2 < 3 IQR (CV) : 2 (0.4)
1:510(42.1%)
2:364(30.1%)
3:337(27.8%)
0 (0%)
6 DOSCC [numeric] Mean (sd) : 4.4 (1.2) min < med < max: 1.6 < 4.3 < 8.6 IQR (CV) : 1.6 (0.3) 401 distinct values 0 (0%)
7 DODIM [numeric] Mean (sd) : 325 (45.8) min < med < max: 252 < 306 < 584 IQR (CV) : 49.5 (0.1) 179 distinct values 0 (0%)
8 PrevCM [numeric] Min : 0 Mean : 0.1 Max : 1
0:1046(86.4%)
1:165(13.6%)
0 (0%)
9 PrevSCCHI [numeric] Mean (sd) : 5.4 (1.3) min < med < max: 2.9 < 5.3 < 9.2 IQR (CV) : 1.8 (0.2) 629 distinct values 0 (0%)
10 DPlength [numeric] Mean (sd) : 55.7 (7.9) min < med < max: 30 < 56 < 87 IQR (CV) : 9 (0.1) 54 distinct values 0 (0%)

Generated by summarytools 0.9.3 (R version 3.6.0)
2019-10-05

Descriptive statistics of subjects at enrollment

Comparison of demographics for each treatment group at dry-off

library(table1)

Attaching package: ‘table1’

The following objects are masked from ‘package:qualityTools’:

    units, units<-

The following objects are masked from ‘package:Hmisc’:

    label, label<-, units

The following objects are masked from ‘package:base’:

    units, units<-
table1(~ Age + DOMY + DOSCC + PrevSCCHI + factor(PrevCM) + factor(Parity) | Tx, data=Baseline)
0
(n=1568)
1
(n=1592)
2
(n=1544)
Overall
(n=4704)
Age
Mean (SD) 47.2 (14.6) 46.9 (15.9) 46.1 (15.0) 46.7 (15.2)
Median [Min, Max] 44.7 [30.8, 104] 44.1 [30.4, 111] 44.5 [30.4, 122] 44.4 [30.4, 122]
DOMY
Mean (SD) 26.7 (8.87) 27.9 (8.81) 27.3 (8.38) 27.3 (8.70)
Median [Min, Max] 27.7 [4.54, 49.4] 29.0 [1.81, 49.4] 29.0 [2.72, 49.4] 28.6 [1.81, 49.4]
DOSCC
Mean (SD) 4.45 (1.21) 4.38 (1.23) 4.45 (1.22) 4.43 (1.22)
Median [Min, Max] 4.33 [1.61, 8.35] 4.23 [1.61, 8.59] 4.39 [1.61, 8.25] 4.32 [1.61, 8.59]
PrevSCCHI
Mean (SD) 5.37 (1.30) 5.49 (1.23) 5.40 (1.29) 5.42 (1.28)
Median [Min, Max] 5.23 [2.87, 9.21] 5.37 [3.14, 9.21] 5.30 [2.94, 9.21] 5.30 [2.87, 9.21]
factor(PrevCM)
0 1344 (85.7%) 1360 (85.4%) 1352 (87.6%) 4056 (86.2%)
1 224 (14.3%) 232 (14.6%) 192 (12.4%) 648 (13.8%)
factor(Parity)
1 616 (39.3%) 732 (46.0%) 660 (42.7%) 2008 (42.7%)
2 516 (32.9%) 416 (26.1%) 488 (31.6%) 1420 (30.2%)
3 436 (27.8%) 444 (27.9%) 396 (25.6%) 1276 (27.1%)

Descriptive statistics of subjects at dry-off

Note that this table excludes cows (n=32) that were not included cow-level analysis (eg. cows with long or short dry periods).

table1(~ Age + DOMY + DPlength + DOSCC + PrevSCCHI + PrevCM + Parity | Tx, data=SDCTCOW)
Blanket
(n=407)
Culture
(n=410)
Algorithm
(n=394)
Overall
(n=1211)
Age
Mean (SD) 47.5 (15.0) 47.2 (16.2) 46.3 (15.1) 47.0 (15.4)
Median [Min, Max] 44.8 [30.8, 114] 44.4 [30.4, 119] 44.6 [30.4, 122] 44.5 [30.4, 122]
DOMY
Mean (SD) 26.8 (8.88) 28.0 (8.89) 27.3 (8.38) 27.4 (8.73)
Median [Min, Max] 27.7 [4.54, 49.4] 29.0 [1.81, 49.4] 29.0 [2.72, 49.4] 29.0 [1.81, 49.4]
DPlength
Mean (SD) 55.3 (7.89) 55.9 (7.61) 55.9 (8.16) 55.7 (7.88)
Median [Min, Max] 56.0 [33.0, 84.0] 56.0 [33.0, 84.0] 56.0 [30.0, 87.0] 56.0 [30.0, 87.0]
DOSCC
Mean (SD) 4.46 (1.22) 4.39 (1.22) 4.45 (1.21) 4.43 (1.22)
Median [Min, Max] 4.36 [1.61, 8.35] 4.23 [1.61, 8.59] 4.39 [1.61, 8.25] 4.33 [1.61, 8.59]
PrevSCCHI
Mean (SD) 5.40 (1.32) 5.50 (1.22) 5.40 (1.29) 5.43 (1.28)
Median [Min, Max] 5.23 [2.87, 9.21] 5.37 [3.14, 9.21] 5.30 [2.94, 9.21] 5.30 [2.87, 9.21]
PrevCM
0 350 (86.0%) 351 (85.6%) 345 (87.6%) 1046 (86.4%)
1 57 (14.0%) 59 (14.4%) 49 (12.4%) 165 (13.6%)
Parity
1 158 (38.8%) 185 (45.1%) 167 (42.4%) 510 (42.1%)
2 133 (32.7%) 108 (26.3%) 123 (31.2%) 364 (30.1%)
3 116 (28.5%) 117 (28.5%) 104 (26.4%) 337 (27.8%)

Groups appear to be well balanced before and after exclusions, indicating that randomization was successful, and that drop-out is unlikely to affect our assumption of exchangeability between treatment groups.





Comparison of herds

library(table1)
table1(~ Tx + Age + DOMY + DPlength + DODIM + DOSCC + PrevSCCHI + PrevCM + Parity | FARMID, data=SDCTCOW)
1
(n=76)
2
(n=82)
3
(n=263)
4
(n=388)
5
(n=242)
6
(n=47)
7
(n=113)
Overall
(n=1211)
Tx
Blanket 28 (36.8%) 27 (32.9%) 93 (35.4%) 122 (31.4%) 81 (33.5%) 16 (34.0%) 40 (35.4%) 407 (33.6%)
Culture 27 (35.5%) 24 (29.3%) 87 (33.1%) 136 (35.1%) 84 (34.7%) 16 (34.0%) 36 (31.9%) 410 (33.9%)
Algorithm 21 (27.6%) 31 (37.8%) 83 (31.6%) 130 (33.5%) 77 (31.8%) 15 (31.9%) 37 (32.7%) 394 (32.5%)
Age
Mean (SD) 48.7 (16.0) 46.8 (14.3) 46.8 (13.4) 47.5 (16.7) 47.0 (15.9) 42.9 (11.2) 46.6 (16.2) 47.0 (15.4)
Median [Min, Max] 45.2 [30.6, 90.2] 44.6 [30.7, 95.7] 44.8 [30.4, 95.5] 44.6 [31.7, 122] 44.7 [30.4, 115] 43.7 [31.0, 82.6] 44.6 [31.0, 114] 44.5 [30.4, 122]
DOMY
Mean (SD) 23.0 (6.30) 26.6 (9.64) 29.5 (6.91) 30.3 (7.84) 19.6 (8.55) 30.7 (4.81) 30.6 (6.33) 27.4 (8.73)
Median [Min, Max] 22.7 [9.07, 38.1] 28.6 [2.72, 44.0] 30.4 [8.62, 47.6] 30.4 [2.72, 49.4] 20.0 [1.81, 39.9] 30.8 [16.8, 40.8] 30.8 [15.4, 48.5] 29.0 [1.81, 49.4]
DPlength
Mean (SD) 53.2 (11.8) 52.5 (5.63) 57.8 (6.39) 55.6 (6.49) 55.7 (8.16) 60.3 (7.19) 53.0 (10.6) 55.7 (7.88)
Median [Min, Max] 52.0 [32.0, 85.0] 53.0 [30.0, 63.0] 58.0 [35.0, 87.0] 56.0 [35.0, 74.0] 55.0 [35.0, 85.0] 60.0 [47.0, 84.0] 55.0 [33.0, 77.0] 56.0 [30.0, 87.0]
DODIM
Mean (SD) 346 (51.4) 334 (52.7) 314 (37.9) 325 (44.4) 329 (51.2) 328 (43.4) 321 (39.1) 325 (45.8)
Median [Min, Max] 326 [292, 584] 304 [293, 512] 293 [266, 475] 296 [283, 468] 308 [252, 512] 314 [258, 444] 307 [272, 476] 306 [252, 584]
DOSCC
Mean (SD) 4.54 (1.04) 4.08 (1.15) 4.00 (0.907) 4.47 (1.16) 5.18 (1.39) 4.34 (0.966) 3.91 (1.09) 4.43 (1.22)
Median [Min, Max] 4.61 [2.56, 7.59] 3.96 [2.30, 8.17] 3.98 [2.60, 6.68] 4.48 [1.61, 8.59] 5.13 [1.61, 8.35] 4.47 [2.56, 6.61] 3.78 [2.56, 7.38] 4.33 [1.61, 8.59]
PrevSCCHI
Mean (SD) 5.48 (1.31) 5.06 (1.31) 4.77 (1.08) 5.77 (1.20) 6.13 (1.11) 5.02 (0.927) 4.73 (1.17) 5.43 (1.28)
Median [Min, Max] 5.31 [3.43, 9.21] 4.78 [3.33, 9.21] 4.61 [2.87, 8.21] 5.65 [3.00, 9.21] 6.07 [3.40, 9.21] 5.09 [3.09, 7.06] 4.53 [2.94, 8.00] 5.30 [2.87, 9.21]
PrevCM
0 62 (81.6%) 81 (98.8%) 228 (86.7%) 337 (86.9%) 191 (78.9%) 46 (97.9%) 101 (89.4%) 1046 (86.4%)
1 14 (18.4%) 1 (1.2%) 35 (13.3%) 51 (13.1%) 51 (21.1%) 1 (2.1%) 12 (10.6%) 165 (13.6%)
Parity
1 31 (40.8%) 33 (40.2%) 92 (35.0%) 180 (46.4%) 104 (43.0%) 23 (48.9%) 47 (41.6%) 510 (42.1%)
2 15 (19.7%) 28 (34.1%) 95 (36.1%) 101 (26.0%) 73 (30.2%) 17 (36.2%) 35 (31.0%) 364 (30.1%)
3 30 (39.5%) 21 (25.6%) 76 (28.9%) 107 (27.6%) 65 (26.9%) 7 (14.9%) 31 (27.4%) 337 (27.8%)

Outcome 1: Clinical mastitis

Kaplan Meier curve & log rank test for clinical mastitis

Kaplan Meier curve

library(ggplot2)
library(survminer)
Loading required package: ggpubr
Loading required package: magrittr

Attaching package: ‘magrittr’

The following object is masked from ‘package:purrr’:

    set_names

The following object is masked from ‘package:tidyr’:

    extract
KM <- survfit(Surv(CMTAR, CM) ~ Tx, data = SDCTCOW)

knitr::opts_chunk$set(fig.width = 800, fig.height = 900)
ggsurvplot(KM, data = SDCTCOW,  title = "", pval = T, conf.int = F,risk.table.col = "Tx",risk.table = T, risk.table.y.text.col = TRUE , surv.plot.height = 5, legend.labs = c("Blanket","Culture","Algorithm"), tables.theme = theme_cleantable(), ggtheme = theme_bw())





Log-Rank test

survdiff(Surv(CMTAR, CM) ~ Tx,data=SDCTCOW,rho=0)
Call:
survdiff(formula = Surv(CMTAR, CM) ~ Tx, data = SDCTCOW, rho = 0)

               N Observed Expected (O-E)^2/E (O-E)^2/V
Tx=Blanket   407       59       52     0.954     1.428
Tx=Culture   410       50       54     0.298     0.454
Tx=Algorithm 394       48       51     0.180     0.267

 Chisq= 1.4  on 2 degrees of freedom, p= 0.5 

Cox proportional hazards regression for clinical mastitis (1-120 DIM)

Model building plan

Model type: Cox proportional hazards analysis with farm included as a cluster variable (robust sandwich standard error estimator) to account for lack of indepedence.

Step 1: Identify potential confouders using a directed acyclic graph (DAG)

Step 2: Identify correlated variables using pearson and kendalls correlation coefficients

Step 3: Create model with all potential confounders

Step 4: Investigate if covariates meet proportional hazards assumption

Step 5: Investigate potential effect measure modification

Step 6: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if hazard ratio for algorithm or culture changes by >10% after removing the covariate, the covariate is retained in the model)

Step 7: Report final model

Step 1: DAG for clincal mastitis

This is used to identify variables that could be confounders if they are not balanced between treatment groups.

library(DiagrammeR)
mermaid("graph LR
        T(Treatment)-->U(Clinical mastitis)
        A(Age)-->T
        P(Parity)-->T
        M(Yield at dry-off)-->T
        S(SCC during prev lactation)-->T
        C(CM in prev lact)-->T
        A-->U
        P-->U
        M-->U
        S-->U
        C-->U
        C-->M
        P-->C
        P-->S
        P-->M
        A-->P
        A-->C
        A-->S
        A-->M
        M-->S
        C-->S
        style A fill:#FFFFFF, stroke-width:0px
        style T fill:#FFFFFF, stroke-width:2px
        style P fill:#FFFFFF, stroke-width:0px
        style M fill:#FFFFFF, stroke-width:0px
        style S fill:#FFFFFF, stroke-width:0px
        style C fill:#FFFFFF, stroke-width:0px
        style I fill:#FFFFFF, stroke-width:0px
        style U fill:#FFFFFF, stroke-width:2px
        ")

According to this DAG, I may need to control for the following variables.

Parity [“Parity”]

Age [“Age”]

Yield at most recent test before dry off [“DOMY”]

Somatic cell count at last herd test during previous lactation [“DOSCC” or “PrevSCCHi”] <- likely to be correlated

Clinical mastitis in previous lactation [“PrevCM”]





Step 2: Identify correlated covariates

Pearson correlation matrix among potential predictors

cor <- BL[, c(4,5,6,7,9,10)]
cor <- cor(cor, use = "complete.obs")
round(cor, 2)
            Age Parity DOSCC DODIM PrevSCCHI DPlength
Age        1.00   0.88  0.29  0.11      0.25    -0.09
Parity     0.88   1.00  0.31  0.01      0.22    -0.11
DOSCC      0.29   0.31  1.00  0.12      0.64    -0.05
DODIM      0.11   0.01  0.12  1.00      0.18    -0.05
PrevSCCHI  0.25   0.22  0.64  0.18      1.00    -0.06
DPlength  -0.09  -0.11 -0.05 -0.05     -0.06     1.00
cor <- BL[, c(4,5,6,7,9,10)]
cor <- cor(cor, use = "complete.obs", method="kendal")
round(cor, 2)
            Age Parity DOSCC DODIM PrevSCCHI DPlength
Age        1.00   0.81  0.24  0.14      0.18    -0.09
Parity     0.81   1.00  0.27  0.02      0.18    -0.11
DOSCC      0.24   0.27  1.00  0.06      0.48    -0.06
DODIM      0.14   0.02  0.06  1.00      0.12    -0.09
PrevSCCHI  0.18   0.18  0.48  0.12      1.00    -0.06
DPlength  -0.09  -0.11 -0.06 -0.09     -0.06     1.00

Age and Parity highly correlated as expected. Will only offer parity.

Previous lactation peak SCC is moderately correlated with SCC at last herd test (DOSCC). Will only offer DOSCC.





Step 3: Create model with all potential covariates

Cox proportional hazards regression for clinical mastitis (1-120 DIM)

Cows that did not calve or that had long/short dry periods are excluded. Cows with clinical mastitis prior to calving are included.

Reasons for R censor = 120 DIM or culling/death

library(broom)
library(survival)
SR <- coxph(Surv(CMTAR, CM) ~ Parity + DOMY + DOSCC + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
coxph(Surv(CMTAR, CM) ~ Parity + DOMY + DOSCC + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
Call:
coxph(formula = Surv(CMTAR, CM) ~ Parity + DOMY + DOSCC + PrevCM + 
    Tx + cluster(FARMID), data = SDCTCOW)

                 coef exp(coef)  se(coef) robust se      z      p
Parity2      0.262972  1.300790  0.198272  0.127747  2.059 0.0395
Parity3      0.328493  1.388873  0.204918  0.292867  1.122 0.2620
DOMY        -0.006115  0.993904  0.010031  0.018794 -0.325 0.7449
DOSCC        0.028361  1.028767  0.076123  0.105980  0.268 0.7890
PrevCM1      0.357508  1.429761  0.212265  0.228486  1.565 0.1177
TxCulture   -0.193527  0.824048  0.192911  0.177916 -1.088 0.2767
TxAlgorithm -0.173991  0.840304  0.194505  0.162762 -1.069 0.2851

Likelihood ratio test=10.21  on 7 df, p=0.1771
n= 1211, number of events= 157 
#tidy(coxph(Surv(CMTAR, CM) ~ Tx + cluster(FARMID), data=SDCTCOW))

Step 4: Schoenfield tests to assess assumption of proportional hazards for explanatory variables.

Parity, Tx and DOSCC violate the assumption of proportional hazards

SR <- cox.zph(SR)
SR
                rho  chisq        p
Parity2     -0.1172  4.313 0.037831
Parity3     -0.1245 11.662 0.000638
DOMY         0.0370  1.843 0.174616
DOSCC        0.1043  5.489 0.019134
PrevCM1      0.0207  0.394 0.530189
TxCulture    0.1564  9.946 0.001612
TxAlgorithm  0.0207  0.480 0.488505
GLOBAL           NA 14.007 0.051053





Schoenfield residual plots to assess assumption of proportional hazards.

ggcoxzph(SR,var = c("TxCulture","TxAlgorithm"))

ggcoxzph(SR,var = c("DOSCC", "DOMY"))

ggcoxzph(SR,var = c("Parity2","Parity3"))

ggcoxzph(SR,var = c("PrevCM1"))





I will deal with these covariates using stratification (i.e. fitting seperate baseline hazards)

I must create categorical variables to allow for this (not shown here).

Dry off milk yield [“DOMY”] -> median split (“DOMYcat” = 0 / 1).

Dry off SCC - split at 200,000 cells (subclinical mastitis [“DOSCM”] = 0 / 1)





Show new variables

SDCTCOWcheck <- SDCTCOW %>% select(Tx,CM,CMTAR,Cull2,Cull2TAR,DOSCC,DOSCM,DOMY,DOMYcat,Parity,PrevCM)
head(SDCTCOWcheck)





Run new cox model with stratified variables

SR <- coxph(Surv(CMTAR, CM) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
tidy(coxph(Surv(CMTAR, CM) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))





Repeat Schoenfeld residuals

Tx no longer p < 0.05, but is close to the threshold (p = 0.08).

SR <- cox.zph(SR)
SR
               rho chisq      p
PrevCM1     0.0273 0.185 0.6674
TxCulture   0.1393 3.094 0.0786
TxAlgorithm 0.0442 0.419 0.5173
GLOBAL          NA 3.320 0.3449





Will split time into 1-60 and 61-120 DIM to see if this difference is meaningful.

Cox model 1-60 DIM

Beta coefficient for Culture = -0.43, Algorithm = -0.08

SR <- coxph(Surv(CMTAR60, CM60) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
tidy(coxph(Surv(CMTAR60, CM60) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))





Cox model 61-120 DIM Beta coefficient for Culture = 0.008, Algorithm = -.401

SR <- coxph(Surv(CMTAR60120, CM60120) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
tidy(coxph(Surv(CMTAR60120, CM60120) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))

Decision: These differences aren’t sufficient in my opinion to warrant pursuing the 1-60, 61-120 DIM models. An average of the two is appropriate.



Step 5: Investigate effect measure modification

Unable to evluate interaction between Tx & FARMID using Cox regression - Bizzare SE’s, won’t converge.

mm0 <- coxph(Surv(CMTAR, CM) ~ Tx + FARMID + Tx:FARMID + PrevCM + strata(Parity) + strata(DOMYcat) + strata(DOSCM), data=SDCTCOW)
Loglik converged before variable  19 ; coefficient may be infinite. 
tidy(mm0)





Will use logistic regression to assess for interaction between Tx and farm: P > 0.05.

mm0 <- glm(CM ~ Tx*FARMID + PrevCM + Parity + DOMYcat + DOSCM, data=SDCTCOW, family=binomial)
car::Anova(mm0)
Analysis of Deviance Table (Type II tests)

Response: CM
          LR Chisq Df Pr(>Chisq)    
Tx           0.881  2     0.6437    
FARMID      35.339  6  3.704e-06 ***
PrevCM       0.763  1     0.3824    
Parity       1.923  2     0.3823    
DOMYcat      1.466  1     0.2260    
DOSCM        0.757  1     0.3843    
Tx:FARMID   12.592 12     0.3994    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Decision: No treatment by herd effect measure modification





Assess effect measure modification with previous clinical mastitis using Cox regression.


a <- coxph(Surv(CMTAR, CM) ~ factor(Tx)*factor(PrevCM) + strata(Parity) + cluster(FARMID) + strata(DOMYcat) + strata(DOSCM), data=SDCTCOW)

library(aod)

Attaching package: ‘aod’

The following object is masked from ‘package:survival’:

    rats
wald.test(b = coef(a), Sigma = vcov(a), Terms = 4:5)
Wald test:
----------

Chi-squared test:
X2 = 11.0, df = 2, P(> X2) = 0.004

Wald test for interaction is p < 0.05.



Model output with interaction

mm0 <- coxph(Surv(CMTAR, CM) ~ Tx*PrevCM + strata(Parity) + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW)
tidy(mm0)

According to this interaction model, the HR (referent = Blanket Tx, no prev CM) for each group are:

Blanket:Prev0 = 1

Blanket:Prev1 = 2.1

Culture:PrevCM0 = 0.93

Culture:PrevCM1 = 0.97

Algorithm:PrevCM0 = 0.93

Algorithm:PrevCM1 = 1.14

This is a counter-intuitive result: hazards of clinical mastitis are higher in blanket cows with previous history of CM.

However, these effect estimates have wide confidence intervals, and this interaction model adds unnecessary complexity and does not change our conclusions.

Decision: Report main effects.





Step 6: Remove unnecessary covariates (backwards selection using 10% rule)

The order for removing covariates will be in increasing likelihood of being a confounder, which is based on my knowledge about the variables and their distribution in treatment groups.

This order will be: DOMYcat, DOSCM, Parity, PrevCM

Step 6a: Full model

mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)) %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0





Step 6b: removing DOMYcat

mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ strata(Parity) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))%>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0

Both HR (Culture and Algorithm) changed by <10%. DOMYcat stays out.



Step 6c: removing DOSCM

mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ strata(Parity) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)) %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0

Both HR changed by <10%. DOMYcat stays out.



Step 6d: removing Parity

mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ PrevCM + Tx + cluster(FARMID), data=SDCTCOW)) %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0

Both HR changed by <10%. Parity stays out.





Step 6e: removing PrevCM

mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ Tx + cluster(FARMID), data=SDCTCOW)) %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0

Both HR changed by <10%. PrevCM stays out.



Step 7a: Reporting final cox model for clinical mastitis (1-120 DIM)

No covariates included, as no evidence for confounding.


CoxCM <- tidy(coxph(Surv(CMTAR, CM) ~ Tx + cluster(FARMID), data=SDCTCOW))
CoxCM$HR <- exp(CoxCM$estimate)
CoxCM$LCL <- exp(CoxCM$conf.low)
CoxCM$UCL <- exp(CoxCM$conf.high)
CoxCM <- CoxCM %>% select(term,HR,LCL,UCL,robust.se,p.value)
CoxCM

Checking Schoenfield residuals for Tx in final model

SR <- coxph(Surv(CMTAR, CM) ~ Tx + cluster(FARMID), data=SDCTCOW)
cox.zph(SR)
                 rho    chisq     p
TxCulture    0.12471 2.077891 0.149
TxAlgorithm -0.00225 0.000429 0.983
GLOBAL            NA 2.596282 0.273
SR <- cox.zph(SR)
ggcoxzph(SR,var = c("TxCulture","TxAlgorithm"))

Sufficient evidence to use Cox model.

Step 7b: Reporting final cox model for clinical mastitis (1-120 DIM) using P-value based backwards stepwise selection

CoxCM <- coxph(Surv(CMTAR, CM) ~ Tx + Parity + cluster(FARMID), data=SDCTCOW) %>% tidy()
CoxCM$HR <- exp(CoxCM$estimate)
CoxCM$LCL <- exp(CoxCM$conf.low)
CoxCM$UCL <- exp(CoxCM$conf.high)
CoxCM <- CoxCM %>% select(term,HR,LCL,UCL,robust.se,p.value)
CoxCM

Estimates are very similar to those found using 10% rule.



Outcome 2: Culling / Death

Kaplan Meier curve & log rank test for culling/death

Kaplan Meier curve

KM <- survfit(Surv(Cull2TAR, Cull2) ~ Tx, data = SDCTCOW)
ggsurvplot(KM, data = SDCTCOW,  title = "", pval = T, conf.int = F,risk.table.col = "Tx",risk.table = T, risk.table.y.text.col = TRUE , surv.plot.height = 5, legend.labs = c("Blanket","Culture","Algorithm"), tables.theme = theme_cleantable(), ggtheme = theme_bw())





Log-Rank test

survdiff(Surv(Cull2TAR, Cull2) ~ Tx,data=SDCTCOW,rho=0)
Call:
survdiff(formula = Surv(Cull2TAR, Cull2) ~ Tx, data = SDCTCOW, 
    rho = 0)

               N Observed Expected (O-E)^2/E (O-E)^2/V
Tx=Blanket   407       44     42.1    0.0891     0.134
Tx=Culture   410       40     43.0    0.2128     0.323
Tx=Algorithm 394       42     40.9    0.0290     0.043

 Chisq= 0.3  on 2 degrees of freedom, p= 0.8 

Cox proportional hazards regression for culling or death (1-120 DIM)

Model building plan

Model type: Cox proportional hazards analysis with farm included as a cluster variable to account for lack of indepedence.

Step 1: Identify potential confouders using a directed acyclic graph (DAG)

Step 2: Identify correlated variables using pearson and kendalls correlation coefficients

Step 3: Create model with all potential confounders

Step 4: Investigate if covariates meet proportional hazards assumption

Step 5: Investigate potential effect measure modification

Step 6: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if HR changes by >10% after removal of covariate, the covariate is retained in the model)

Step 7: Report final model

Steps 1 & 2: Identify potential confouders using a directed acyclic graph (DAG)

library(DiagrammeR)
mermaid("graph LR
        T(Treatment)-->U(Culling or Death)
        A(Age)-->T
        P(Parity)-->T
        M(Yield at dry-off)-->T
        S(SCC during prev lactation)-->T
        C(CM in prev lact)-->T
        A-->U
        P-->U
        M-->U
        S-->U
        C-->U
        C-->M
        P-->C
        P-->S
        P-->M
        A-->P
        A-->C
        A-->S
        A-->M
        M-->S
        C-->S
        style A fill:#FFFFFF, stroke-width:0px
        style T fill:#FFFFFF, stroke-width:2px
        style P fill:#FFFFFF, stroke-width:0px
        style M fill:#FFFFFF, stroke-width:0px
        style S fill:#FFFFFF, stroke-width:0px
        style C fill:#FFFFFF, stroke-width:0px
        style I fill:#FFFFFF, stroke-width:0px
        style U fill:#FFFFFF, stroke-width:2px
        ")

According to this DAG, I may need to control for the following variables:

Parity [“Parity”]. Will not offer Age [“Age”] as it is highly correlated.

Yield at most recent test before dry off [“DOMY”]

Somatic cell count at last herd test during previous lactation [“DOSCC”] <- will not offer PrevSCCHI as it was correlated with DOSCC

Clinical mastitis in previous lactation [“PrevCM”]





Step 3: Create model with all potential confounders

Cows that did not calve are excluded (left censored)

Reason for R censor = 120 DIM

library(broom)
library(survival)
coxph(Surv(Cull2TAR, Cull2) ~ Parity + DOMY + DOSCC + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
Call:
coxph(formula = Surv(Cull2TAR, Cull2) ~ Parity + DOMY + DOSCC + 
    PrevCM + Tx + cluster(FARMID), data = SDCTCOW)

                coef exp(coef) se(coef) robust se      z        p
Parity2      0.39524   1.48475  0.25866   0.21257  1.859  0.06298
Parity3      1.13923   3.12436  0.23351   0.23115  4.929 8.29e-07
DOMY        -0.01446   0.98564  0.01107   0.01471 -0.983  0.32560
DOSCC        0.08981   1.09396  0.08514   0.05241  1.714  0.08660
PrevCM1      0.26788   1.30719  0.22819   0.09322  2.874  0.00406
TxCulture   -0.09850   0.90619  0.21940   0.21233 -0.464  0.64271
TxAlgorithm  0.01074   1.01079  0.21583   0.23312  0.046  0.96327

Likelihood ratio test=44.51  on 7 df, p=1.706e-07
n= 1211, number of events= 126 





Step 4: Investigate if covariates meet proportional hazards assumption

Both DOSCC and DOMY don’t meet the assumption of proportional hazards

SR <- cox.zph(coxph(Surv(Cull2TAR, Cull2) ~ Parity + DOMY + DOSCC + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))
SR
                rho chisq       p
Parity2     -0.1157 2.607 0.10639
Parity3     -0.0343 0.209 0.64753
DOMY         0.1521 7.402 0.00652
DOSCC        0.1462 5.471 0.01934
PrevCM1     -0.1220 2.530 0.11172
TxCulture    0.1222 3.313 0.06872
TxAlgorithm  0.0815 1.396 0.23741
GLOBAL           NA 8.182 0.31686

Schoenfield residual plots

ggcoxzph(SR,var = c("TxCulture","TxAlgorithm"))





DOSCC and DOMY don’t meet the assumption of proportional hazards

ggcoxzph(SR,var = c("DOSCC", "DOMY"))

ggcoxzph(SR,var = c("Parity2","Parity3"))

ggcoxzph(SR,var = c("PrevCM1"))





Refit cox model with seperate baselines (stratified) for DOMY and DOSCC.

No evidence of other time-varying covariates or predictors (Tx).

SR <- coxph(Surv(Cull2TAR, Cull2) ~ Parity + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
SR <- cox.zph(SR)
SR
                 rho    chisq     p
Parity2     -0.05884 0.412749 0.521
Parity3     -0.00113 0.000217 0.988
PrevCM1     -0.06962 0.500950 0.479
TxCulture    0.10086 1.689182 0.194
TxAlgorithm  0.07741 1.091294 0.296
GLOBAL            NA 2.214228 0.819





Step 5: Assess for effect measure modification

Tx : FARMID - could not assess this using Cox regression as model did not converge or reported unusually large SEs for some interaction terms.

SR <- coxph(Surv(Cull2TAR, Cull2) ~ Tx*FARMID + Parity + PrevCM + Parity + strata(DOMYcat) + strata(DOSCM), data=SDCTCOW)
Loglik converged before variable  20 ; coefficient may be infinite. 
tidy(SR)





I will assess effect Tx:farm interaction using logistic regression:

Wald test for interaction term was P > 0.05.

mm0 <- glm(CM ~ Tx*FARMID + Parity + PrevCM + Parity + DOMYcat + DOSCM, data=SDCTCOW)
car::Anova(mm0)
Analysis of Deviance Table (Type II tests)

Response: CM
          LR Chisq Df Pr(>Chisq)    
Tx           0.924  2     0.6300    
FARMID      33.573  6  8.132e-06 ***
Parity       1.953  2     0.3767    
PrevCM       1.039  1     0.3082    
DOMYcat      1.573  1     0.2097    
DOSCM        0.810  1     0.3683    
Tx:FARMID   10.174 12     0.6007    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1





Assess for other interactions using Wald testfrom Cox regression.

Wald test was P > 0.05 for Tx:PrevCM interaction .

mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx*PrevCM + Parity + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW)
summary(mm0)
Call:
coxph(formula = Surv(Cull2TAR, Cull2) ~ Tx * PrevCM + Parity + 
    strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data = SDCTCOW)

  n= 1211, number of events= 126 

                        coef exp(coef) se(coef) robust se      z Pr(>|z|)    
TxCulture           -0.02411   0.97618  0.24667   0.23595 -0.102   0.9186    
TxAlgorithm          0.05495   1.05649  0.24266   0.27674  0.199   0.8426    
PrevCM1              0.49435   1.63943  0.36416   0.20400  2.423   0.0154 *  
Parity2              0.41575   1.51550  0.25731   0.21398  1.943   0.0520 .  
Parity3              1.17829   3.24881  0.23075   0.25675  4.589 4.45e-06 ***
TxCulture:PrevCM1   -0.40970   0.66385  0.53890   0.33877 -1.209   0.2265    
TxAlgorithm:PrevCM1 -0.21937   0.80303  0.53502   0.70719 -0.310   0.7564    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

                    exp(coef) exp(-coef) lower .95 upper .95
TxCulture              0.9762     1.0244    0.6147     1.550
TxAlgorithm            1.0565     0.9465    0.6142     1.817
PrevCM1                1.6394     0.6100    1.0991     2.445
Parity2                1.5155     0.6598    0.9964     2.305
Parity3                3.2488     0.3078    1.9642     5.374
TxCulture:PrevCM1      0.6638     1.5064    0.3417     1.290
TxAlgorithm:PrevCM1    0.8030     1.2453    0.2008     3.211

Concordance= 0.64  (se = 0.03 )
Likelihood ratio test= 33.79  on 7 df,   p=2e-05
Wald test            = 1281  on 7 df,   p=<2e-16
Score (logrank) test = 36.55  on 7 df,   p=6e-06,   Robust = 7  p=0.4

  (Note: the likelihood ratio and score tests assume independence of
     observations within a cluster, the Wald and robust score tests do not).
wald.test(b = coef(mm0), Sigma = vcov(mm0), Terms = 6:7)
Wald test:
----------

Chi-squared test:
X2 = 1.6, df = 2, P(> X2) = 0.46





Wald test was P < 0.05 for Tx:Parity interaction .

mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx*Parity + PrevCM + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW)
summary(mm0)
Call:
coxph(formula = Surv(Cull2TAR, Cull2) ~ Tx * Parity + PrevCM + 
    strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data = SDCTCOW)

  n= 1211, number of events= 126 

                       coef exp(coef) se(coef) robust se      z Pr(>|z|)    
TxCulture            0.5382    1.7130   0.5005    0.4124  1.305 0.191869    
TxAlgorithm          0.5758    1.7786   0.5080    0.5537  1.040 0.298327    
Parity2              0.8960    2.4498   0.4961    0.4546  1.971 0.048749 *  
Parity3              1.7523    5.7680   0.4572    0.4022  4.357 1.32e-05 ***
PrevCM1              0.3018    1.3522   0.2277    0.1047  2.882 0.003946 ** 
TxCulture:Parity2   -0.6590    0.5173   0.6640    0.7136 -0.924 0.355691    
TxAlgorithm:Parity2 -0.6252    0.5352   0.6531    0.6359 -0.983 0.325518    
TxCulture:Parity3   -0.8959    0.4082   0.5861    0.2552 -3.511 0.000446 ***
TxAlgorithm:Parity3 -0.7392    0.4775   0.5900    0.4252 -1.739 0.082111 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

                    exp(coef) exp(-coef) lower .95 upper .95
TxCulture              1.7130     0.5838    0.7633    3.8440
TxAlgorithm            1.7786     0.5622    0.6009    5.2648
Parity2                2.4498     0.4082    1.0049    5.9721
Parity3                5.7680     0.1734    2.6224   12.6871
PrevCM1                1.3522     0.7395    1.1014    1.6602
TxCulture:Parity2      0.5173     1.9329    0.1278    2.0949
TxAlgorithm:Parity2    0.5352     1.8686    0.1539    1.8610
TxCulture:Parity3      0.4082     2.4496    0.2476    0.6731
TxAlgorithm:Parity3    0.4775     2.0943    0.2075    1.0987

Concordance= 0.651  (se = 0.025 )
Likelihood ratio test= 35.95  on 9 df,   p=4e-05
Wald test            = 89593  on 9 df,   p=<2e-16
Score (logrank) test = 38.57  on 9 df,   p=1e-05,   Robust = 7  p=0.6

  (Note: the likelihood ratio and score tests assume independence of
     observations within a cluster, the Wald and robust score tests do not).
wald.test(b = coef(mm0), Sigma = vcov(mm0), Terms = 6:9)
Wald test:
----------

Chi-squared test:
X2 = 658.3, df = 4, P(> X2) = 0.0




Investigate potential effect measure modification by doing stratified models

Parity = 1 Frequency table

table(SDCTCOW$Tx[SDCTCOW$Parity==1],SDCTCOW$Cull2[SDCTCOW$Parity==1])
           
              0   1
  Blanket   152   6
  Culture   173  12
  Algorithm 156  11




Model (Parity = 1)

mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW[SDCTCOW$Parity==1,]) %>% tidy()
mm0$HR <- exp(mm0$estimate)
mm0$LCL <- exp(mm0$conf.low)
mm0$UCL <- exp(mm0$conf.high)
mm0 %>% select("term","HR","LCL","UCL")




Parity = 2

Frequency table

table(SDCTCOW$Tx[SDCTCOW$Parity==2],SDCTCOW$Cull2[SDCTCOW$Parity==2])
           
              0   1
  Blanket   120  13
  Culture    99   9
  Algorithm 112  11
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW[SDCTCOW$Parity==2,]) %>% tidy()
mm0$HR <- exp(mm0$estimate)
mm0$LCL <- exp(mm0$conf.low)
mm0$UCL <- exp(mm0$conf.high)
mm0 %>% select("term","HR","LCL","UCL")




Parity = 3 or greater

Frequency table

table(SDCTCOW$Tx[SDCTCOW$Parity==3],SDCTCOW$Cull2[SDCTCOW$Parity==3])
           
             0  1
  Blanket   91 25
  Culture   98 19
  Algorithm 84 20
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW[SDCTCOW$Parity==3,]) %>% tidy
mm0$HR <- exp(mm0$estimate)
mm0$LCL <- exp(mm0$conf.low)
mm0$UCL <- exp(mm0$conf.high)
mm0 %>% select("term","HR","LCL","UCL")

This finding suggests that potential culling risks associated with SDCT may be higher in parity 1 cows than in multiparous animals. However these HR estimates in all 3 parity groups are imprecise (wide confidence intervals) because of a small number of culling/death events. For example, in lactation 1 animals: 6 in BDCT, 11 in Algorithm and 12 in Culture. Therefore, this difference in effects across levels of parity may be due to chance alone, and not worth investigating too closely.

Decision: Report main effects.




Step 6: Remove unnecessary covariates (backwards selection using 10% rule)

The order for removing covariates will be in increasing likelihood of being a confounder, which is based on my knowledge about the variables and their distribution in treatment groups.

This order will be: DOMYcat, DOSCM, PrevCM, Parity

Step 6a: Full model

mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + Parity + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0





Step 6b: removing DOMYcat

mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + Parity + strata(DOSCM) + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0

HR for culture and algorithm didn’t change by >10%. DOMYcat stays out.



Step 6c: removing DOSCM

mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + Parity + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0

HR changed by <10%. DOSCM stays out.



Step 6d: removing PrevCM

mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + Parity + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0

HR changed by <10%. Leave PrevCM out.



Step 6e: removing Parity

mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0

HR changed by <10%. Parity stays out.





Step 7a: Final cox model for culling or death (1 - 120 DIM)

No covariates included, as no evidence for confounding.

CoxCull <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + cluster(FARMID), data=SDCTCOW) %>% tidy()
CoxCull$HR <- exp(CoxCull$estimate)
CoxCull$LCL <- exp(CoxCull$conf.low)
CoxCull$UCL <- exp(CoxCull$conf.high)
CoxCull <- CoxCull %>% select(term,HR,LCL,UCL,robust.se,p.value)
CoxCull

Check schoenfield residuals for final model

SR <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + cluster(FARMID), data=SDCTCOW)
cox.zph(SR)
               rho chisq     p
TxCulture   0.1100  1.52 0.217
TxAlgorithm 0.0951  1.12 0.290
GLOBAL          NA  1.53 0.466
SR <- cox.zph(SR)
ggcoxzph(SR,var = c("TxCulture","TxAlgorithm"))

Step 7b: Final cox model for culling or death (1 - 120 DIM) using P-value based backwards stepwise selection

CoxCull <- coxph(Surv(CullTAR, Cull2) ~ Tx + Parity + DOSCC + PrevCM + cluster(FARMID), data=SDCTCOW) %>% tidy()
CoxCull$HR <- exp(CoxCull$estimate)
CoxCull$LCL <- exp(CoxCull$conf.low)
CoxCull$UCL <- exp(CoxCull$conf.high)
CoxCull <- CoxCull %>% select(term,HR,LCL,UCL,robust.se,p.value)
CoxCull

Estimates are similar to 10% rule based approach



Changing datasets: DHI dataset with multiple rows per cow

Dataset example

SDCTCOWDHI$Tx <- 
  factor(SDCTCOWDHI$Tx, 
         levels=c(0,1,2),
         labels=c("Blanket",
                  "Culture", 
                  "Algorithm"))

DHIcheck <- SDCTCOWDHI %>% select(Tx,CowID,FARMID,DIM,TestDIMcat20,LSCC,MY,Parity,PrevCM,DOMY,DOSCC)
head(DHIcheck, n=10)





Inspect data

DHIoutcome <- SDCTCOWDHI %>% select(SCC,MY,SCM)
DHIoutcome$logSCC <- log(DHIoutcome$SCC + 1)
#summarytools::dfSummary(DHIoutcome, style='grid')
print(summarytools::dfSummary(DHIoutcome, valid.col=FALSE, graph.magnif=0.8, style="grid"), method = "render")

Data Frame Summary

DHIoutcome

Dimensions: 3992 x 4
Duplicates: 967
No Variable Stats / Values Freqs (% of Valid) Graph Missing
1 SCC [numeric] Mean (sd) : 184.4 (678.2) min < med < max: 0 < 39 < 9999 IQR (CV) : 89 (3.7) 608 distinct values 3 (0.08%)
2 MY [numeric] Mean (sd) : 49.1 (10.5) min < med < max: 0.9 < 49.4 < 93.4 IQR (CV) : 13.2 (0.2) 149 distinct values 2 (0.05%)
3 SCM [numeric] Min : 0 Mean : 0.1 Max : 1
0:3409(85.5%)
1:580(14.5%)
3 (0.08%)
4 logSCC [numeric] Mean (sd) : 3.9 (1.4) min < med < max: 0 < 3.7 < 9.2 IQR (CV) : 1.7 (0.3) 608 distinct values 3 (0.08%)

Generated by summarytools 0.9.3 (R version 3.6.0)
2019-10-05

NA

Very little missing data. Will do complete case analysis.



Assessing normality for continuous outcome variables

Somatic cell count (log x 10,000 cells)

qqPlot(log(SDCTCOWDHI$SCC+1))

hist(log(SDCTCOWDHI$SCC+1))





Milk yield (kg)

qqPlot(SDCTCOWDHI$MY)

hist(SDCTCOWDHI$MY)





Outcome 3: Somatic cell count

Modelling plan

Model type: Linear mixed models, random intercepts for farm and cow will be fitted to account for repeated measures within cows, and clustering of cows within herds

Step 1: Identify potential confouders using a directed acyclic graph (DAG)

Step 2: Identify correlated variables using pearson and kendalls correlation coefficients

Step 3: Create model with all potential confounders

Step 4: Investigate potential effect measure modification

Step 5: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if estimated difference in SCC changes by >10% after removing the covariate, the covariate is retained in the model)

Step 6: Report final model

Step 7: Model diagnostics

Step 1 & 2 Identify potential confounders using a DAG

library(DiagrammeR)
mermaid("graph LR
        T(Treatment)-->U(SCC)
        A(Age)-->T
        P(Parity)-->T
        M(Yield at dry-off)-->T
        S(SCC during prev lactation)-->T
        C(CM in prev lact)-->T
        D(Days in milk at test)-->U
        D-->T
        A-->U
        P-->U
        M-->U
        S-->U
        C-->U
        C-->M
        P-->C
        P-->S
        P-->M
        A-->P
        A-->C
        A-->S
        A-->M
        M-->S
        C-->S
        style A fill:#FFFFFF, stroke-width:0px
        style T fill:#FFFFFF, stroke-width:2px
        style P fill:#FFFFFF, stroke-width:0px
        style M fill:#FFFFFF, stroke-width:0px
        style S fill:#FFFFFF, stroke-width:0px
        style C fill:#FFFFFF, stroke-width:0px
        style I fill:#FFFFFF, stroke-width:0px
        style D fill:#FFFFFF, stroke-width:0px
        style U fill:#FFFFFF, stroke-width:2px
        ")

According to this DAG, I may need to control for the following variables:

Parity [“Parity”] <- Age not offered as highly correlated

Yield at most recent test before dry off [“DOMY”]

Somatic cell count at last herd test during previous lactation [“DOSCC”] <- PrevSCCHI not offered as correlated

Clinical mastitis in previous lactation [“PrevCM”]

Days in milk at herd test (category, 0-20 “10”, 21-40 “30” etc) [“TestDIMcat20”]





Step 3: Create model with all potential confounders

mm0 <- lmer(LSCC ~ Tx + TestDIMcat20 + Parity + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
summary(mm0)
Linear mixed model fit by REML ['lmerMod']
Formula: LSCC ~ Tx + TestDIMcat20 + Parity + DOSCC + DOMY + PrevCM + (1 |      FARMID/CowID)
   Data: SDCTCOWDHI

REML criterion at convergence: 13110.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.5975 -0.4985 -0.1040  0.4340  3.9735 

Random effects:
 Groups       Name        Variance Std.Dev.
 CowID:FARMID (Intercept) 0.61791  0.7861  
 FARMID       (Intercept) 0.02027  0.1424  
 Residual                 1.14078  1.0681  
Number of obs: 3989, groups:  CowID:FARMID, 1178; FARMID, 7

Fixed effects:
                 Estimate Std. Error t value
(Intercept)      3.338254   0.204372  16.334
TxCulture        0.047878   0.070138   0.683
TxAlgorithm      0.074745   0.070822   1.055
TestDIMcat2030  -0.576961   0.063393  -9.101
TestDIMcat2050  -0.557223   0.060950  -9.142
TestDIMcat2070  -0.394721   0.059969  -6.582
TestDIMcat2090  -0.272158   0.065089  -4.181
TestDIMcat20110 -0.084757   0.060209  -1.408
Parity2          0.110743   0.070611   1.568
Parity3          0.259957   0.074986   3.467
DOSCC            0.139922   0.028350   4.935
DOMY             0.002402   0.003983   0.603
PrevCM1          0.361076   0.087707   4.117

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
car::vif(mm0)
                 GVIF Df GVIF^(1/(2*Df))
Tx           1.009521  2        1.002372
TestDIMcat20 1.003238  5        1.000323
Parity       1.141466  2        1.033631
DOSCC        1.319455  1        1.148676
DOMY         1.167395  1        1.080461
PrevCM       1.050427  1        1.024903





Step 4: Investigate effect measure modification

Tx:FARM (P > 0.05)

mm0 <- lmer(LSCC ~ Tx*FARMID + Parity + TestDIMcat20 + DOSCC + DOMY + PrevCM + (1|CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: LSCC
                Chisq Df Pr(>Chisq)    
Tx             0.3270  2   0.849151    
FARMID        20.8837  6   0.001925 ** 
Parity        10.7805  2   0.004561 ** 
TestDIMcat20 153.2866  5  < 2.2e-16 ***
DOSCC         23.5900  1  1.192e-06 ***
DOMY           0.1511  1   0.697525    
PrevCM        16.3381  1  5.299e-05 ***
Tx:FARMID     13.6785 12   0.321709    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1





Tx:DIM category at herd test (P > 0.05)

mm0 <- lmer(LSCC ~ Tx*TestDIMcat20 + Parity + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: LSCC
                   Chisq Df Pr(>Chisq)    
Tx                1.1452  2    0.56405    
TestDIMcat20    155.5912  5  < 2.2e-16 ***
Parity           12.0313  2    0.00244 ** 
DOSCC            24.5071  1  7.404e-07 ***
DOMY              0.3514  1    0.55332    
PrevCM           16.9005  1  3.939e-05 ***
Tx:TestDIMcat20   3.6320 10    0.96242    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1





Tx:Parity (P > 0.05)

mm0 <- lmer(LSCC ~ Tx*Parity + TestDIMcat20 + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: LSCC
                Chisq Df Pr(>Chisq)    
Tx             1.1474  2   0.563433    
Parity        12.0289  2   0.002443 ** 
TestDIMcat20 155.4765  5  < 2.2e-16 ***
DOSCC         25.0949  1  5.458e-07 ***
DOMY           0.4871  1   0.485238    
PrevCM        16.3909  1  5.153e-05 ***
Tx:Parity      5.3325  4   0.254853    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1





Tx:PrevCM (P > 0.05)

mm0 <- lmer(LSCC ~ Tx*PrevCM + Parity + TestDIMcat20 + DOSCC + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: LSCC
                Chisq Df Pr(>Chisq)    
Tx             1.1470  2   0.563549    
PrevCM        16.9457  1  3.846e-05 ***
Parity        12.3024  2   0.002131 ** 
TestDIMcat20 155.7581  5  < 2.2e-16 ***
DOSCC         23.9345  1  9.967e-07 ***
DOMY           0.2841  1   0.594020    
Tx:PrevCM      1.1795  2   0.554478    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1





Tx:DOMY (P > 0.05)

mm0 <- lmer(LSCC ~ Tx*DOMY + PrevCM + Parity + TestDIMcat20 + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: LSCC
                Chisq Df Pr(>Chisq)    
Tx             1.1481  2    0.56324    
DOMY           0.3580  1    0.54964    
PrevCM        17.4500  1   2.95e-05 ***
Parity        11.7208  2    0.00285 ** 
TestDIMcat20 155.5513  5  < 2.2e-16 ***
DOSCC         24.5607  1   7.20e-07 ***
Tx:DOMY        3.2738  2    0.19458    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Step 5: Remove unneccesary covariates in backwards stepwise fashion using 10% rule

The order for removing covariates will be in increasing likelihood of being a confounder, which is based on my knowledge about the variables and their distribution in treatment groups.

This order will be: DOMY, Parity, PrevCM, DOSCC

TestDIMcat20 will not be removed.

Step 5a: Full model

mm0 <- lmer(LSCC ~ Tx + PrevCM + Parity + TestDIMcat20 + DOSCC + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
mm0 %>% tidy()
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector





Step 5b: removing DOMY

mm0 <- lmer(LSCC ~ Tx + PrevCM + Parity + TestDIMcat20 + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0%>% tidy()
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

Changed by <10%. DOMY stays out.



Step 5b: removing Parity

mm0 <- lmer(LSCC ~ Tx + PrevCM + TestDIMcat20 + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI)
mm0 %>% tidy()
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

Changed by <10%. Parity stays out.





Step 5c: removing PrevCM

mm0 <- lmer(LSCC ~ Tx + TestDIMcat20 + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy()
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

Changed by >10%. PrevCM stays in.



Step 5d: removing DOSCC

mm0 <- lmer(LSCC ~ Tx + PrevCM + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
mm0 %>% tidy()
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

Changed by > 10%. DOSCC stays in.



Step 6a: Final model for SCC (1 - 120 DIM)

mm0 <- lmer(LSCC ~ Tx + PrevCM + DOSCC + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
mm0 %>% tidy(conf.int=TRUE)
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

ICC for SCC (1 - 120 DIM)

mm0 <- lmer(LSCC ~ 1 + (1|FARMID/CowID), data=SDCTCOWDHI)
summary(mm0)
Linear mixed model fit by REML ['lmerMod']
Formula: LSCC ~ 1 + (1 | FARMID/CowID)
   Data: SDCTCOWDHI

REML criterion at convergence: 13293.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.0159 -0.5107 -0.1062  0.4452  4.0999 

Random effects:
 Groups       Name        Variance Std.Dev.
 CowID:FARMID (Intercept) 0.65871  0.8116  
 FARMID       (Intercept) 0.03917  0.1979  
 Residual                 1.20343  1.0970  
Number of obs: 3989, groups:  CowID:FARMID, 1178; FARMID, 7

Fixed effects:
            Estimate Std. Error t value
(Intercept)  3.86908    0.08308   46.57

ICC (CowID) = 0.35 ICC (FARMID) = 0.02

Most clustering is happening within cow, which is not a suprise given this is longitudinal data.

Step 6b: Final model for SCC (1 - 120 DIM) using P-value based backwards selection

lmer(LSCC ~ Tx + Parity + PrevCM + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI) %>% summary()
Linear mixed model fit by REML ['lmerMod']
Formula: LSCC ~ Tx + Parity + PrevCM + DOSCC + (1 | FARMID/CowID)
   Data: SDCTCOWDHI

REML criterion at convergence: 13233.2

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.1671 -0.5100 -0.1122  0.4512  4.1458 

Random effects:
 Groups       Name        Variance Std.Dev.
 CowID:FARMID (Intercept) 0.59501  0.7714  
 FARMID       (Intercept) 0.01825  0.1351  
 Residual                 1.20377  1.0972  
Number of obs: 3989, groups:  CowID:FARMID, 1178; FARMID, 7

Fixed effects:
            Estimate Std. Error t value
(Intercept)  3.12018    0.13160  23.710
TxCulture    0.04063    0.06986   0.582
TxAlgorithm  0.06227    0.07063   0.882
Parity2      0.11211    0.07042   1.592
Parity3      0.25300    0.07477   3.384
PrevCM1      0.37041    0.08730   4.243
DOSCC        0.13267    0.02635   5.035

Correlation of Fixed Effects:
            (Intr) TxCltr TxAlgr Party2 Party3 PrvCM1
TxCulture   -0.298                                   
TxAlgorithm -0.270  0.498                            
Parity2     -0.042  0.054  0.021                     
Parity3      0.038  0.012  0.019  0.439              
PrevCM1      0.069 -0.019  0.013 -0.044 -0.100       
DOSCC       -0.786  0.026  0.000 -0.223 -0.295 -0.143
lmer(LSCC ~ Tx + Parity + PrevCM + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI) %>% car::Anova() %>% tidy()
NA

Estimates are very similar to 10% rule based approach.



Step 6c: Final model (using 10% rule) reported as estimated marginal means (~LSmeans)

Mean log SCC

mm0 <- lmer(LSCC ~ Tx + PrevCM + DOSCC + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
emm <- emmeans(mm0, ~Tx) %>% tidy()
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(pbkrtest.limit = 3989) or larger,
but be warned that this may result in large computation time and memory use.
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(lmerTest.limit = 3989) or larger,
but be warned that this may result in large computation time and memory use.
emm

Step 6c: Final model (using 10% rule) reported as back-transformed estimated marginal means (~LSmeans)

Geometric mean SCC

mm0 <- lmer(LSCC ~ Tx + PrevCM + DOSCC + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
emm <- emmeans(mm0, ~Tx) %>% tidy()
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(pbkrtest.limit = 3989) or larger,
but be warned that this may result in large computation time and memory use.
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(lmerTest.limit = 3989) or larger,
but be warned that this may result in large computation time and memory use.
emm$SCC <- exp(emm$estimate) 
emm$LCL <- exp(emm$asymp.LCL)
emm$UCL <- exp(emm$asymp.UCL)
emm <- emm %>% select(Tx,SCC,LCL,UCL)
emm




Reported as back-transformed estimated marginal means by herd test day, no interaction with test DIM

mm0 <- lmer(LSCC ~ Tx + TestDIMcat20 + DOSCC + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
atx <- c(10,30,50,70,90,110)
emm <- emmeans(mm0, ~Tx*TestDIMcat20, at=list(atx)) %>% tidy()
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(pbkrtest.limit = 3989) or larger,
but be warned that this may result in large computation time and memory use.
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(lmerTest.limit = 3989) or larger,
but be warned that this may result in large computation time and memory use.
emm$SCC <- exp(emm$estimate)
emm$LCL <- exp(emm$asymp.LCL)
emm$UCL <- exp(emm$asymp.UCL)
emm <- emm %>% select(Tx,TestDIMcat20,SCC,LCL,UCL)
curve <- ggplot(emm) + coord_cartesian(ylim = (c(0,100))) + aes(x=TestDIMcat20, y=SCC, group=Tx, colour=Tx) + geom_point() + geom_line(aes(colour=Tx,linetype=Tx)) + geom_ribbon(aes(ymin=emm$LCL, ymax=emm$UCL,colour=Tx,fill=Tx), linetype=0, alpha=0.1)
curve





Reported as back-transformed estimated marginal means by herd test day, with interaction with test DIM

mm0 <- lmer(LSCC ~ Tx*TestDIMcat20 + PrevCM + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI)
atx <- c(10,30,50,70,90,110)
emm <- emmeans(mm0, ~Tx*TestDIMcat20, at=list(atx)) %>% tidy()
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(pbkrtest.limit = 3989) or larger,
but be warned that this may result in large computation time and memory use.
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(lmerTest.limit = 3989) or larger,
but be warned that this may result in large computation time and memory use.
emm$SCC <- exp(emm$estimate)
emm$LCL <- exp(emm$asymp.LCL)
emm$UCL <- exp(emm$asymp.UCL)
emm <- emm %>% select(Tx,TestDIMcat20,SCC,LCL,UCL)
curve <- ggplot(emm) + coord_cartesian(ylim = (c(0,100))) + aes(x=TestDIMcat20, y=SCC, group=Tx, colour=Tx) + geom_point() + geom_line(aes(colour=Tx,linetype=Tx)) + geom_ribbon(aes(ymin=emm$LCL, ymax=emm$UCL,colour=Tx,fill=Tx), linetype=0, alpha=0.1)
curve





Step 7: Model diagnostics

Checking homoskedasticity assumption (variance of residuals)

mm0 <- lmer(LSCC ~ Tx + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
ggplot(data.frame(eta=predict(mm0,type="link"),pearson=residuals(mm0,type="pearson")),
       aes(x=eta,y=pearson)) +
  geom_point() +
  theme_bw()

Checking normality of residuals

qqnorm(residuals(mm0))

Evidence of small L tail. Although some evidence of heteroskedasticity and not perfectly normal residuals, I believe these are allowable for this model.

Outcome 4: Milk yield

Modelling plan

Model type: Linear mixed models, random intercepts for farm and cow will be fitted to account for repeated measures within cows, and clustering of cows within herds

Step 1: Identify potential confouders using a directed acyclic graph (DAG)

Step 2: Identify correlated variables using pearson and kendalls correlation coefficients

Step 3: Create model with all potential confounders

Step 4: Investigate potential effect measure modification

Step 5: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if estimated difference in milk yield changes by >10% after removing the covariate, the covariate is retained in the model)

Step 6: Report final model

Step 7: Model diagnostics

Step 1 & 2 Identify potential confounders using a DAG

library(DiagrammeR)
mermaid("graph LR
        T(Treatment)-->U(Milk yield)
        A(Age)-->T
        P(Parity)-->T
        M(Yield at dry-off)-->T
        S(SCC during prev lactation)-->T
        C(CM in prev lact)-->T
        D(Days in milk at test)-->U
        D-->T
        A-->U
        P-->U
        M-->U
        S-->U
        C-->U
        C-->M
        P-->C
        P-->S
        P-->M
        A-->P
        A-->C
        A-->S
        A-->M
        M-->S
        C-->S
        style A fill:#FFFFFF, stroke-width:0px
        style T fill:#FFFFFF, stroke-width:2px
        style P fill:#FFFFFF, stroke-width:0px
        style M fill:#FFFFFF, stroke-width:0px
        style S fill:#FFFFFF, stroke-width:0px
        style C fill:#FFFFFF, stroke-width:0px
        style I fill:#FFFFFF, stroke-width:0px
        style D fill:#FFFFFF, stroke-width:0px
        style U fill:#FFFFFF, stroke-width:2px
        ")

According to this DAG, I may need to control for the following variables:

Parity [“Parity”] <- Age not offered as highly correlated

Yield at most recent test before dry off [“DOMY”]

Somatic cell count at last herd test during previous lactation [“DOSCC”] <- PrevSCCHI not offered as correlated

Clinical mastitis in previous lactation [“PrevCM”]

Days in milk at herd test (category, 0-20 “10”, 21-40 “30” etc) [“TestDIMcat20”]





Step 3: Create a model with all potential covariates

mm0 <- lmer(MY ~ Tx + TestDIMcat20 + Parity + DOSCC + PrevCM + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
summary(mm0)
Linear mixed model fit by REML ['lmerMod']
Formula: MY ~ Tx + TestDIMcat20 + Parity + DOSCC + PrevCM + DOMY + (1 |      FARMID/CowID)
   Data: SDCTCOWDHI

REML criterion at convergence: 27948.5

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.3698 -0.4620  0.0223  0.5283  3.9851 

Random effects:
 Groups       Name        Variance Std.Dev.
 CowID:FARMID (Intercept) 28.70    5.357   
 FARMID       (Intercept)  9.63    3.103   
 Residual                 46.18    6.795   
Number of obs: 3990, groups:  CowID:FARMID, 1177; FARMID, 7

Fixed effects:
                Estimate Std. Error t value
(Intercept)     30.22473    1.76719  17.103
TxCulture       -0.04144    0.46718  -0.089
TxAlgorithm     -0.92795    0.47146  -1.968
TestDIMcat2030  11.86182    0.40548  29.253
TestDIMcat2050  12.87916    0.38854  33.148
TestDIMcat2070  12.51208    0.38249  32.713
TestDIMcat2090  11.01316    0.41572  26.492
TestDIMcat20110  8.43431    0.38401  21.964
Parity2          2.52549    0.47112   5.361
Parity3          3.01851    0.50067   6.029
DOSCC            0.26481    0.19029   1.392
PrevCM1         -0.24232    0.58620  -0.413
DOMY             0.22068    0.02706   8.156

Correlation matrix not shown by default, as p = 13 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it
car::vif(mm0)
                 GVIF Df GVIF^(1/(2*Df))
Tx           1.009493  2        1.002365
TestDIMcat20 1.002987  5        1.000298
Parity       1.145893  2        1.034632
DOSCC        1.308164  1        1.143750
PrevCM       1.048252  1        1.023842
DOMY         1.154875  1        1.074651





Step 4: Investigate effect measure modification

Tx:FARM (P < 0.05)

mm0 <- lmer(MY ~ Tx*FARMID + Parity + TestDIMcat20 + DOSCC + DOMY + PrevCM + (1|CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: MY
                 Chisq Df Pr(>Chisq)    
Tx              7.1919  2    0.02743 *  
FARMID        383.1701  6  < 2.2e-16 ***
Parity         56.0941  2  6.597e-13 ***
TestDIMcat20 1502.4062  5  < 2.2e-16 ***
DOSCC           1.8384  1    0.17514    
DOMY           73.6534  1  < 2.2e-16 ***
PrevCM          0.2286  1    0.63260    
Tx:FARMID      21.1764 12    0.04786 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Significant interaction term.

Descision: Revisit this after covariates are finalized.



Tx:DIM category at herd test (P > 0.05)

mm0 <- lmer(MY ~ Tx*TestDIMcat20 + Parity + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: MY
                    Chisq Df Pr(>Chisq)    
Tx                 4.9281  2    0.08509 .  
TestDIMcat20    1563.6373  5  < 2.2e-16 ***
Parity            45.3091  2  1.450e-10 ***
DOSCC              1.8538  1    0.17335    
DOMY              65.8173  1  4.947e-16 ***
PrevCM             0.1793  1    0.67194    
Tx:TestDIMcat20   11.3951 10    0.32757    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1





Tx:Parity (P > 0.05)

mm0 <- lmer(MY ~ Tx*Parity + TestDIMcat20 + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: MY
                 Chisq Df Pr(>Chisq)    
Tx              4.9461  2    0.08433 .  
Parity         45.4964  2   1.32e-10 ***
TestDIMcat20 1563.4543  5  < 2.2e-16 ***
DOSCC           2.2956  1    0.12974    
DOMY           68.0948  1  < 2.2e-16 ***
PrevCM          0.2483  1    0.61826    
Tx:Parity       6.9870  4    0.13658    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1





Tx:PrevCM (P > 0.05)

mm0 <- lmer(MY ~ Tx*PrevCM + Parity + TestDIMcat20 + DOSCC + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: MY
                 Chisq Df Pr(>Chisq)    
Tx              4.9345  2    0.08482 .  
PrevCM          0.1709  1    0.67934    
Parity         45.4975  2  1.319e-10 ***
TestDIMcat20 1561.6764  5  < 2.2e-16 ***
DOSCC           2.0081  1    0.15647    
DOMY           67.3721  1  2.248e-16 ***
Tx:PrevCM       1.6370  2    0.44109    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1





Step 5: Remove unnecessary covariates using backwards selection (10% rule)

The order for removing covariates will be in increasing likelihood of being a confounder, which is based on my knowledge about the variables and their distribution in treatment groups.

This order will be: DOSCC, PrevCM, Parity, DOMY

TestDIMcat20 will not be removed (forced into model).

Step 5a: Full model

mm0 <- lmer(MY ~ Tx + PrevCM + Parity + TestDIMcat20 + DOSCC + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy() %>% select(term,estimate)
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector





Step 5b: Removing DOSCC

mm0 <- lmer(MY ~ Tx + PrevCM + Parity + TestDIMcat20 + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy() %>% select(term,estimate)
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

Changed by <10%. DOSCC stays out



Step 5c: removing PrevCM

mm0 <- lmer(MY ~ Tx + Parity + TestDIMcat20 + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)  
mm0 %>% tidy() %>% select(term,estimate)
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

Changed by < 10%. PrevCM stays out.





Step 5d: removing Parity

mm0 <- lmer(MY ~ Tx + TestDIMcat20 + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy() %>% select(term,estimate)
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

Changed by >10%. Parity stays in.


Step 5e: removing DOMY

mm0 <- lmer(MY ~ Tx + Parity + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy() %>% select(term,estimate)
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

Changed by >10%. DOMY stays in.



Revisit effect measure modification previously identified

Effect measure modification with herd (P < 0.05)

mm0 <- lmer(MY ~ Tx*FARMID + TestDIMcat20 + Parity + DOMY + (1|CowID), data=SDCTCOWDHI)
car::Anova(mm0)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: MY
                 Chisq Df Pr(>Chisq)    
Tx              7.0355  2    0.02967 *  
FARMID        409.5611  6  < 2.2e-16 ***
TestDIMcat20 1502.2612  5  < 2.2e-16 ***
Parity         70.6857  2  4.475e-16 ***
DOMY           74.5582  1  < 2.2e-16 ***
Tx:FARMID      21.1553 12    0.04815 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Decision - will investigate effect estimates stratified by herd



Step 6a: Final model for milk yield (1 - 120 DIM), stratified by herd.

Model output

mm0 <- lmer(MY ~ Tx*FARMID + TestDIMcat20 + Parity + DOMY + (1|CowID), data=SDCTCOWDHI)
emmeans(mm0,pairwise ~ Tx | FARMID)
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(pbkrtest.limit = 3990) or larger,
but be warned that this may result in large computation time and memory use.
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(lmerTest.limit = 3990) or larger,
but be warned that this may result in large computation time and memory use.
$emmeans
FARMID = 1:
 Tx        emmean    SE  df asymp.LCL asymp.UCL
 Blanket     47.4 1.240 Inf      45.0      49.8
 Culture     49.7 1.162 Inf      47.4      51.9
 Algorithm   46.2 1.381 Inf      43.5      48.9

FARMID = 2:
 Tx        emmean    SE  df asymp.LCL asymp.UCL
 Blanket     49.6 1.200 Inf      47.3      52.0
 Culture     46.0 1.300 Inf      43.4      48.5
 Algorithm   43.4 1.188 Inf      41.1      45.8

FARMID = 3:
 Tx        emmean    SE  df asymp.LCL asymp.UCL
 Blanket     43.4 0.703 Inf      42.1      44.8
 Culture     43.8 0.701 Inf      42.4      45.1
 Algorithm   42.0 0.736 Inf      40.6      43.5

FARMID = 4:
 Tx        emmean    SE  df asymp.LCL asymp.UCL
 Blanket     53.3 0.565 Inf      52.2      54.4
 Culture     52.5 0.534 Inf      51.4      53.5
 Algorithm   53.2 0.558 Inf      52.2      54.3

FARMID = 5:
 Tx        emmean    SE  df asymp.LCL asymp.UCL
 Blanket     49.4 0.739 Inf      48.0      50.9
 Culture     49.9 0.712 Inf      48.5      51.3
 Algorithm   48.1 0.752 Inf      46.6      49.5

FARMID = 6:
 Tx        emmean    SE  df asymp.LCL asymp.UCL
 Blanket     49.2 1.515 Inf      46.2      52.1
 Culture     52.3 1.548 Inf      49.2      55.3
 Algorithm   50.7 1.698 Inf      47.4      54.1

FARMID = 7:
 Tx        emmean    SE  df asymp.LCL asymp.UCL
 Blanket     50.4 1.014 Inf      48.4      52.4
 Culture     49.4 1.066 Inf      47.3      51.5
 Algorithm   49.2 1.067 Inf      47.1      51.2

Results are averaged over the levels of: TestDIMcat20, Parity 
Degrees-of-freedom method: asymptotic 
Confidence level used: 0.95 

$contrasts
FARMID = 1:
 contrast            estimate    SE  df z.ratio p.value
 Blanket - Culture    -2.2771 1.693 Inf -1.345  0.3704 
 Blanket - Algorithm   1.1734 1.848 Inf  0.635  0.8008 
 Culture - Algorithm   3.4506 1.800 Inf  1.917  0.1337 

FARMID = 2:
 contrast            estimate    SE  df z.ratio p.value
 Blanket - Culture     3.6627 1.767 Inf  2.072  0.0956 
 Blanket - Algorithm   6.2020 1.686 Inf  3.678  0.0007 
 Culture - Algorithm   2.5393 1.758 Inf  1.444  0.3182 

FARMID = 3:
 contrast            estimate    SE  df z.ratio p.value
 Blanket - Culture    -0.3310 0.990 Inf -0.334  0.9402 
 Blanket - Algorithm   1.4086 1.015 Inf  1.388  0.3474 
 Culture - Algorithm   1.7396 1.015 Inf  1.713  0.2002 

FARMID = 4:
 contrast            estimate    SE  df z.ratio p.value
 Blanket - Culture     0.8679 0.770 Inf  1.128  0.4969 
 Blanket - Algorithm   0.0873 0.786 Inf  0.111  0.9932 
 Culture - Algorithm  -0.7806 0.760 Inf -1.027  0.5600 

FARMID = 5:
 contrast            estimate    SE  df z.ratio p.value
 Blanket - Culture    -0.5102 0.985 Inf -0.518  0.8627 
 Blanket - Algorithm   1.3592 1.015 Inf  1.339  0.3733 
 Culture - Algorithm   1.8695 1.003 Inf  1.863  0.1495 

FARMID = 6:
 contrast            estimate    SE  df z.ratio p.value
 Blanket - Culture    -3.1044 2.164 Inf -1.435  0.3229 
 Blanket - Algorithm  -1.5474 2.273 Inf -0.681  0.7747 
 Culture - Algorithm   1.5571 2.290 Inf  0.680  0.7753 

FARMID = 7:
 contrast            estimate    SE  df z.ratio p.value
 Blanket - Culture     0.9515 1.467 Inf  0.649  0.7931 
 Blanket - Algorithm   1.2379 1.468 Inf  0.843  0.6761 
 Culture - Algorithm   0.2864 1.503 Inf  0.191  0.9802 

Results are averaged over the levels of: TestDIMcat20, Parity 
P value adjustment: tukey method for comparing a family of 3 estimates 

It appears that herd 2 (87 cows) and herd 6 (42 cows) have extreme results compared with the other herds. In herd 2, BDCT had much higher MY than SDCT cows. In herd 6, it was the opposite effect. Given these were the smallest herds in the study, I will report a pooled result.



Step 6bi: Final model reported without herd interaction

Model output

summary(lmer(MY ~ Tx + TestDIMcat20 + Parity + DOMY+ (1|FARMID/CowID), data=SDCTCOWDHI))
Linear mixed model fit by REML ['lmerMod']
Formula: MY ~ Tx + TestDIMcat20 + Parity + DOMY + (1 | FARMID/CowID)
   Data: SDCTCOWDHI

REML criterion at convergence: 27949.8

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.3374 -0.4572  0.0207  0.5284  3.9942 

Random effects:
 Groups       Name        Variance Std.Dev.
 CowID:FARMID (Intercept) 28.677   5.355   
 FARMID       (Intercept)  9.946   3.154   
 Residual                 46.184   6.796   
Number of obs: 3990, groups:  CowID:FARMID, 1177; FARMID, 7

Fixed effects:
                Estimate Std. Error t value
(Intercept)     31.61485    1.47112  21.490
TxCulture       -0.04671    0.46702  -0.100
TxAlgorithm     -0.92025    0.47129  -1.953
TestDIMcat2030  11.86555    0.40548  29.263
TestDIMcat2050  12.87773    0.38856  33.143
TestDIMcat2070  12.51168    0.38250  32.710
TestDIMcat2090  11.01773    0.41571  26.503
TestDIMcat20110  8.43423    0.38402  21.963
Parity2          2.66366    0.45780   5.818
Parity3          3.20325    0.47445   6.752
DOMY             0.20758    0.02539   8.175

Correlation of Fixed Effects:
            (Intr) TxCltr TxAlgr TDIM203 TDIM205 TDIM207 TDIM209 TDIM201 Party2 Party3
TxCulture   -0.132                                                                    
TxAlgorithm -0.146  0.499                                                             
TstDIMc2030 -0.144 -0.013 -0.012                                                      
TstDIMc2050 -0.132 -0.010 -0.013  0.486                                               
TstDIMc2070 -0.135 -0.010 -0.004  0.534   0.481                                       
TstDIMc2090 -0.143 -0.005 -0.005  0.515   0.499   0.471                               
TstDIM20110 -0.129 -0.008 -0.004  0.514   0.507   0.527   0.465                       
Parity2     -0.167  0.055  0.021  0.000   0.008  -0.001   0.004   0.006               
Parity3     -0.173  0.013  0.018 -0.014   0.009  -0.009   0.012  -0.001   0.399       
DOMY        -0.478 -0.065 -0.027  0.013  -0.002  -0.002   0.019  -0.014   0.066  0.101

Model output (tidy)

lmer(MY ~ Tx + TestDIMcat20 + Parity + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI) %>% tidy(conf.int=TRUE)
binding factor and character vector, coercing into character vectorbinding character and factor vector, coercing into character vector

ICC for MY (1 - 120 DIM)

mm0 <- lmer(MY ~ 1 + (1|FARMID/CowID), data=SDCTCOWDHI)
summary(mm0)
Linear mixed model fit by REML ['lmerMod']
Formula: MY ~ 1 + (1 | FARMID/CowID)
   Data: SDCTCOWDHI

REML criterion at convergence: 29310.2

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.1211 -0.4867  0.0849  0.5681  3.5617 

Random effects:
 Groups       Name        Variance Std.Dev.
 CowID:FARMID (Intercept) 27.03    5.199   
 FARMID       (Intercept) 10.06    3.172   
 Residual                 70.88    8.419   
Number of obs: 3990, groups:  CowID:FARMID, 1177; FARMID, 7

Fixed effects:
            Estimate Std. Error t value
(Intercept)   48.286      1.226   39.38

ICC (CowID) = 0.25 ICC (FARMID) = 0.09

Emmeans without TestDIM interaction

mm0 <- lmer(MY ~ Tx + TestDIMcat20 + Parity + DOMY+ (1|FARMID/CowID), data=SDCTCOWDHI)

emmeans(mm0,~Tx) %>% tidy
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(pbkrtest.limit = 3990) or larger,
but be warned that this may result in large computation time and memory use.
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(lmerTest.limit = 3990) or larger,
but be warned that this may result in large computation time and memory use.

Step 6bii: Final model reported without herd interaction (using P-value based backwards elimination)

Model output

summary(lmer(MY ~ Tx + TestDIMcat20 + Parity + (1|FARMID/CowID), data=SDCTCOWDHI))
Linear mixed model fit by REML ['lmerMod']
Formula: MY ~ Tx + TestDIMcat20 + Parity + (1 | FARMID/CowID)
   Data: SDCTCOWDHI

REML criterion at convergence: 28009.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.2353 -0.4645  0.0246  0.5246  3.9839 

Random effects:
 Groups       Name        Variance Std.Dev.
 CowID:FARMID (Intercept) 31.11    5.578   
 FARMID       (Intercept) 11.14    3.338   
 Residual                 46.17    6.795   
Number of obs: 3990, groups:  CowID:FARMID, 1177; FARMID, 7

Fixed effects:
                Estimate Std. Error t value
(Intercept)      37.3558     1.3606  27.456
TxCulture         0.2008     0.4792   0.419
TxAlgorithm      -0.8169     0.4844  -1.687
TestDIMcat2030   11.8422     0.4064  29.139
TestDIMcat2050   12.8803     0.3890  33.113
TestDIMcat2070   12.5248     0.3830  32.704
TestDIMcat2090   10.9596     0.4165  26.315
TestDIMcat20110   8.4713     0.3844  22.040
Parity2           2.4166     0.4697   5.145
Parity3           2.8034     0.4853   5.777

Correlation of Fixed Effects:
            (Intr) TxCltr TxAlgr TDIM203 TDIM205 TDIM207 TDIM209 TDIM201 Party2
TxCulture   -0.182                                                             
TxAlgorithm -0.177  0.499                                                      
TstDIMc2030 -0.150 -0.012 -0.012                                               
TstDIMc2050 -0.144 -0.010 -0.013  0.486                                        
TstDIMc2070 -0.147 -0.010 -0.004  0.535   0.480                                
TstDIMc2090 -0.145 -0.004 -0.005  0.515   0.499   0.470                        
TstDIM20110 -0.147 -0.009 -0.005  0.515   0.507   0.528   0.464                
Parity2     -0.151  0.059  0.022 -0.001   0.008  -0.001   0.003   0.006        
Parity3     -0.139  0.019  0.021 -0.015   0.009  -0.008   0.010   0.000   0.395





Step 6biii: Final model (using 10% rule) reported as estimated marginal means by test DIM category (no interaction with test DIM)

mm0 <- lmer(MY ~ Tx + TestDIMcat20 + Parity + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)

atx <- c(10,30,50,70,90,110)
emm <- emmeans(mm0, ~Tx*TestDIMcat20) %>% tidy()
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(pbkrtest.limit = 3990) or larger,
but be warned that this may result in large computation time and memory use.
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(lmerTest.limit = 3990) or larger,
but be warned that this may result in large computation time and memory use.
emm$MY <- emm$estimate
emm$LCL <- emm$asymp.LCL
emm$UCL <- emm$asymp.UCL
emm %>% select(Tx,TestDIMcat20,MY,LCL,UCL)

Plotting model as predicted values

curve <- ggplot(emm) + coord_cartesian(ylim = (c(0,55))) + aes(x=TestDIMcat20, y=MY, group=Tx, colour=Tx) + geom_point() + geom_line(aes(colour=Tx,linetype=Tx)) + geom_ribbon(aes(ymin=emm$LCL, ymax=emm$UCL,colour=Tx,fill=Tx), linetype=0, alpha=0.1)
curve





Reported as estimated marginal means by test day category with interaction with herd test DIM

mm0 <- lmer(MY ~ Tx*TestDIMcat20 + Parity + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
atx <- c(10,30,50,70,90,110)
emm <- emmeans(mm0, ~Tx*TestDIMcat20, at=list(atx)) %>% tidy()
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(pbkrtest.limit = 3990) or larger,
but be warned that this may result in large computation time and memory use.
Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
To enable adjustments, set emm_options(lmerTest.limit = 3990) or larger,
but be warned that this may result in large computation time and memory use.
emm$MY <- emm$estimate
emm$LCL <- emm$asymp.LCL
emm$UCL <- emm$asymp.UCL
emm <- emm %>% select(Tx,TestDIMcat20,MY,LCL,UCL)

curve <- ggplot(emm) + coord_cartesian(ylim = (c(0,55))) + aes(x=TestDIMcat20, y=MY, group=Tx, colour=Tx) + geom_point() + geom_line(aes(colour=Tx,linetype=Tx)) + geom_ribbon(aes(ymin=emm$LCL, ymax=emm$UCL,colour=Tx,fill=Tx), linetype=0, alpha=0.1)
curve

Step 7: Model diagnostics

Checking homoskedasticity assumption (variance of residuals)

mm0 <- lmer(MY ~ Tx + TestDIMcat20 + Parity +DOMY+ (1|FARMID/CowID), data=SDCTCOWDHI)
ggplot(data.frame(eta=predict(mm0,type="link"),pearson=residuals(mm0,type="pearson")),
       aes(x=eta,y=pearson)) +
  geom_point() +
  theme_bw()

Checking normality of residuals

qqnorm(residuals(mm0))

I am happy with homoskedasticity and normal residuals assumptions

---
title: "Selective Dry Cow Therapy: Cow-level analysis"
output:
  html_notebook:
    toc: true
    toc_depth: 3
    toc_float:
      collapsed: true

---

```{r setup}
#Mac
knitr::opts_knit$set(root.dir = "~/Dropbox/R backup/SDCT - R")

#Windows
#knitr::opts_knit$set(root.dir = "C:/Users/rowe0122/Dropbox/R backup/SDCT - R")

```


```{r}
library(knitr)
```

Load data

```{r}
load(file="Baseline.Rdata")
load(file="SDCTCOW.Rdata")
load(file="SDCTCOWDHI.Rdata")

SDCTCOW = SDCTCOW %>%
  mutate(Tx = recode(SDCTCOW$Tx,
                     "0" = "Blanket", "1" = "Culture", "2" = "Algorithm"))

```


Import file BL (cows included for analysis) for descriptive statistics
```{r}
library(readr)
BL <- read_csv("BL.csv", col_types = cols(X1 = col_skip()))
head(BL)
```
# Inspect data

```{r}
print(summarytools::dfSummary(BL, valid.col=FALSE, graph.magnif=0.8, style="grid"), method = "render")
```

## Descriptive statistics of subjects at enrollment
Comparison of demographics for each treatment group at dry-off
```{r}
library(table1)
table1(~ Age + DOMY + DOSCC + PrevSCCHI + factor(PrevCM) + factor(Parity) | Tx, data=Baseline)
```

## Descriptive statistics of subjects at dry-off
Note that this table excludes cows (n=32) that were not included cow-level analysis (eg. cows with long or short dry periods).
```{r}
table1(~ Age + DOMY + DPlength + DOSCC + PrevSCCHI + PrevCM + Parity | Tx, data=SDCTCOW)
```
Groups appear to be well balanced before and after exclusions, indicating that randomization was successful, and that drop-out is unlikely to affect our assumption of exchangeability between treatment groups.

<br>
<br>
<br>
<br>
Comparison of herds
```{r}
library(table1)
table1(~ Tx + Age + DOMY + DPlength + DODIM + DOSCC + PrevSCCHI + PrevCM + Parity | FARMID, data=SDCTCOW)
```


# Outcome 1: Clinical mastitis
## Kaplan Meier curve & log rank test for clinical mastitis

Kaplan Meier curve
```{r fig.height=8}
library(ggplot2)
library(survminer)
KM <- survfit(Surv(CMTAR, CM) ~ Tx, data = SDCTCOW)

knitr::opts_chunk$set(fig.width = 800, fig.height = 900)
ggsurvplot(KM, data = SDCTCOW,  title = "", pval = T, conf.int = F,risk.table.col = "Tx",risk.table = T, risk.table.y.text.col = TRUE , surv.plot.height = 5, legend.labs = c("Blanket","Culture","Algorithm"), tables.theme = theme_cleantable(), ggtheme = theme_bw())

```
<br>
<br>
<br>
<br>
Log-Rank test
```{r}
survdiff(Surv(CMTAR, CM) ~ Tx,data=SDCTCOW,rho=0)
```


## Cox proportional hazards regression for clinical mastitis (1-120 DIM)
## Model building plan

Model type: Cox proportional hazards analysis with farm included as a cluster variable (robust sandwich standard error estimator) to account for lack of indepedence. 

Step 1: Identify potential confouders using a directed acyclic graph (DAG)

Step 2: Identify correlated variables using pearson and kendalls correlation coefficients

Step 3: Create model with all potential confounders

Step 4: Investigate if covariates meet proportional hazards assumption

Step 5: Investigate potential effect measure modification

Step 6: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if hazard ratio for algorithm or culture changes by >10% after removing the covariate, the covariate is retained in the model)

Step 7: Report final model

### Step 1: DAG for clincal mastitis
This is used to identify variables that could be confounders if they are not balanced between treatment groups. 
```{r fig.width = 10}
library(DiagrammeR)
mermaid("graph LR
        T(Treatment)-->U(Clinical mastitis)
        A(Age)-->T
        P(Parity)-->T
        M(Yield at dry-off)-->T
        S(SCC during prev lactation)-->T
        C(CM in prev lact)-->T
        A-->U
        P-->U
        M-->U
        S-->U
        C-->U
        C-->M
        P-->C
        P-->S
        P-->M
        A-->P
        A-->C
        A-->S
        A-->M
        M-->S
        C-->S
        style A fill:#FFFFFF, stroke-width:0px
        style T fill:#FFFFFF, stroke-width:2px
        style P fill:#FFFFFF, stroke-width:0px
        style M fill:#FFFFFF, stroke-width:0px
        style S fill:#FFFFFF, stroke-width:0px
        style C fill:#FFFFFF, stroke-width:0px
        style I fill:#FFFFFF, stroke-width:0px
        style U fill:#FFFFFF, stroke-width:2px
        ")
```
According to this DAG, I may need to control for the following variables.

Parity ["Parity"]

Age ["Age"]

Yield at most recent test before dry off ["DOMY"]

Somatic cell count at last herd test during previous lactation ["DOSCC" or "PrevSCCHi"] <- likely to be correlated

Clinical mastitis in previous lactation ["PrevCM"]


<br>
<br>
<br>
<br>

### Step 2: Identify correlated covariates
Pearson correlation matrix among potential predictors
```{r}
cor <- BL[, c(4,5,6,7,9,10)]
cor <- cor(cor, use = "complete.obs")
round(cor, 2)
```

```{r}
cor <- BL[, c(4,5,6,7,9,10)]
cor <- cor(cor, use = "complete.obs", method="kendal")
round(cor, 2)
```

Age and Parity highly correlated as expected.  Will only offer parity. 

Previous lactation peak SCC is moderately correlated with SCC at last herd test (DOSCC). Will only offer DOSCC. 

<br>
<br>
<br>
<br>

### Step 3: Create model with all potential covariates
Cox proportional hazards regression for clinical mastitis (1-120 DIM)

Cows that did not calve or that had long/short dry periods are excluded. 
Cows with clinical mastitis prior to calving are included. 

Reasons for R censor = 120 DIM or culling/death

```{r}
library(broom)
library(survival)
SR <- coxph(Surv(CMTAR, CM) ~ Parity + DOMY + DOSCC + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
coxph(Surv(CMTAR, CM) ~ Parity + DOMY + DOSCC + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)

#tidy(coxph(Surv(CMTAR, CM) ~ Tx + cluster(FARMID), data=SDCTCOW))
```

### Step 4: Schoenfield tests to assess assumption of proportional hazards for explanatory variables.

Parity, Tx and DOSCC violate the assumption of proportional hazards
```{r}
SR <- cox.zph(SR)
SR
```
<br>
<br>
<br>
<br>

Schoenfield residual plots to assess assumption of proportional hazards. 
```{r fig.height=8}
ggcoxzph(SR,var = c("TxCulture","TxAlgorithm"))
```

```{r fig.height=8}
ggcoxzph(SR,var = c("DOSCC", "DOMY"))
```
```{r fig.height=8}
ggcoxzph(SR,var = c("Parity2","Parity3"))
```
```{r fig.height=8}
ggcoxzph(SR,var = c("PrevCM1"))
```

<br>
<br>
<br>
<br>
I will deal with these covariates using stratification (i.e. fitting seperate baseline hazards)

I must create categorical variables to allow for this (not shown here). 

Dry off milk yield ["DOMY"] -> median split ("DOMYcat" = 0 / 1).

Dry off SCC - split at 200,000 cells (subclinical mastitis ["DOSCM"] = 0 / 1)

<br>
<br>
<br>
<br>
Show new variables
```{r}
SDCTCOWcheck <- SDCTCOW %>% select(Tx,CM,CMTAR,Cull2,Cull2TAR,DOSCC,DOSCM,DOMY,DOMYcat,Parity,PrevCM)
head(SDCTCOWcheck)
```
<br>
<br>
<br>
<br>

Run new cox model with stratified variables 
```{r}
SR <- coxph(Surv(CMTAR, CM) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
tidy(coxph(Surv(CMTAR, CM) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))
```
<br>
<br>
<br>
<br>
Repeat Schoenfeld residuals

Tx no longer p < 0.05, but is close to the threshold (p = 0.08).
```{r}
SR <- cox.zph(SR)
SR
```
<br>
<br>
<br>
<br>
Will split time into 1-60 and 61-120 DIM to see if this difference is meaningful.

Cox model 1-60 DIM

Beta coefficient for Culture = -0.43, Algorithm = -0.08
```{r}
SR <- coxph(Surv(CMTAR60, CM60) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
tidy(coxph(Surv(CMTAR60, CM60) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))
```
<br>
<br>
<br>
<br>
Cox model 61-120 DIM
Beta coefficient for Culture = 0.008, Algorithm = -.401
```{r}
SR <- coxph(Surv(CMTAR60120, CM60120) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
tidy(coxph(Surv(CMTAR60120, CM60120) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))
```

Decision:  These differences aren't sufficient in my opinion to warrant pursuing the 1-60, 61-120 DIM models. An average of the two is appropriate.
<br>
<br>
<br>
<br>

### Step 5: Investigate effect measure modification

Unable to evluate interaction between Tx & FARMID using Cox regression - Bizzare SE's, won't converge. 
```{r}
mm0 <- coxph(Surv(CMTAR, CM) ~ Tx + FARMID + Tx:FARMID + PrevCM + strata(Parity) + strata(DOMYcat) + strata(DOSCM), data=SDCTCOW)
tidy(mm0)
```
<br>
<br>
<br>
<br>
Will use logistic regression to assess for interaction between Tx and farm: P > 0.05. 
```{r}
mm0 <- glm(CM ~ Tx*FARMID + PrevCM + Parity + DOMYcat + DOSCM, data=SDCTCOW, family=binomial)
car::Anova(mm0)
```

Decision: No treatment by herd effect measure modification

<br>
<br>
<br>
<br>
Assess effect measure modification with previous clinical mastitis using Cox regression. 
```{r}

a <- coxph(Surv(CMTAR, CM) ~ factor(Tx)*factor(PrevCM) + strata(Parity) + cluster(FARMID) + strata(DOMYcat) + strata(DOSCM), data=SDCTCOW)

library(aod)
wald.test(b = coef(a), Sigma = vcov(a), Terms = 4:5)

```

Wald test for interaction is p < 0.05.
<br>
<br>
<br>
<br>
Model output with interaction
```{r}
mm0 <- coxph(Surv(CMTAR, CM) ~ Tx*PrevCM + strata(Parity) + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW)
tidy(mm0)
```
According to this interaction model, the HR (referent = Blanket Tx, no prev CM) for each group are:

Blanket:Prev0 = 1

Blanket:Prev1 = 2.1

Culture:PrevCM0 = 0.93

Culture:PrevCM1 = 0.97

Algorithm:PrevCM0 = 0.93

Algorithm:PrevCM1 = 1.14

This is a counter-intuitive result: hazards of clinical mastitis are higher in blanket cows with previous history of CM.

However, these effect estimates have wide confidence intervals, and this interaction model adds unnecessary complexity and does not change our conclusions. 

Decision: Report main effects. 

<br>
<br>
<br>
<br>

### Step 6: Remove unnecessary covariates (backwards selection using 10% rule)

The order for removing covariates will be in increasing likelihood of being a confounder, which is based on my knowledge about the variables and their distribution in treatment groups.

This order will be: DOMYcat, DOSCM, Parity, PrevCM

Step 6a: Full model
```{r}
mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ strata(Parity) + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)) %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
<br>
<br>
<br>
<br>

Step 6b: removing DOMYcat
```{r}
mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ strata(Parity) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))%>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
Both HR (Culture and Algorithm) changed by <10%. DOMYcat stays out. 
<br>
<br>
<br>
<br>
Step 6c: removing DOSCM
```{r}
mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ strata(Parity) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)) %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
Both HR changed by <10%. DOMYcat stays out. 
<br>
<br>
<br>
<br>

Step 6d: removing Parity
```{r}
mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ PrevCM + Tx + cluster(FARMID), data=SDCTCOW)) %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
Both HR changed by <10%. Parity stays out.

<br>
<br>
<br>
<br>
Step 6e: removing PrevCM
```{r}
mm0 <- tidy(coxph(Surv(CMTAR, CM) ~ Tx + cluster(FARMID), data=SDCTCOW)) %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
Both HR changed by <10%.  PrevCM stays out. 
<br>
<br>
<br>
<br>

### Step 7a: Reporting final cox model for clinical mastitis (1-120 DIM)
No covariates included, as no evidence for confounding.
```{r}

CoxCM <- tidy(coxph(Surv(CMTAR, CM) ~ Tx + cluster(FARMID), data=SDCTCOW))
CoxCM$HR <- exp(CoxCM$estimate)
CoxCM$LCL <- exp(CoxCM$conf.low)
CoxCM$UCL <- exp(CoxCM$conf.high)
CoxCM <- CoxCM %>% select(term,HR,LCL,UCL,robust.se,p.value)
CoxCM
```

#### Checking Schoenfield residuals for Tx in final model
```{r fig.height=8}
SR <- coxph(Surv(CMTAR, CM) ~ Tx + cluster(FARMID), data=SDCTCOW)
cox.zph(SR)
SR <- cox.zph(SR)
ggcoxzph(SR,var = c("TxCulture","TxAlgorithm"))
```
Sufficient evidence to use Cox model.

### Step 7b: Reporting final cox model for clinical mastitis (1-120 DIM) using P-value based backwards stepwise selection
```{r}
CoxCM <- coxph(Surv(CMTAR, CM) ~ Tx + Parity + cluster(FARMID), data=SDCTCOW) %>% tidy()
CoxCM$HR <- exp(CoxCM$estimate)
CoxCM$LCL <- exp(CoxCM$conf.low)
CoxCM$UCL <- exp(CoxCM$conf.high)
CoxCM <- CoxCM %>% select(term,HR,LCL,UCL,robust.se,p.value)
CoxCM
```
Estimates are very similar to those found using 10% rule.
<br>
<br>
<br>
<br>


# Outcome 2: Culling / Death
## Kaplan Meier curve & log rank test for culling/death

Kaplan Meier curve
```{r fig.height=8}
KM <- survfit(Surv(Cull2TAR, Cull2) ~ Tx, data = SDCTCOW)
ggsurvplot(KM, data = SDCTCOW,  title = "", pval = T, conf.int = F,risk.table.col = "Tx",risk.table = T, risk.table.y.text.col = TRUE , surv.plot.height = 5, legend.labs = c("Blanket","Culture","Algorithm"), tables.theme = theme_cleantable(), ggtheme = theme_bw())
```
<br>
<br>
<br>
<br>
Log-Rank test
```{r}
survdiff(Surv(Cull2TAR, Cull2) ~ Tx,data=SDCTCOW,rho=0)
```


## Cox proportional hazards regression for culling or death (1-120 DIM)
## Model building plan

Model type: Cox proportional hazards analysis with farm included as a cluster variable to account for lack of indepedence.

Step 1: Identify potential confouders using a directed acyclic graph (DAG)

Step 2: Identify correlated variables using pearson and kendalls correlation coefficients

Step 3: Create model with all potential confounders

Step 4: Investigate if covariates meet proportional hazards assumption

Step 5: Investigate potential effect measure modification

Step 6: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if HR changes by >10% after removal of covariate, the covariate is retained in the model)

Step 7: Report final model


### Steps 1 & 2: Identify potential confouders using a directed acyclic graph (DAG)
```{r fig.width=10}
library(DiagrammeR)
mermaid("graph LR
        T(Treatment)-->U(Culling or Death)
        A(Age)-->T
        P(Parity)-->T
        M(Yield at dry-off)-->T
        S(SCC during prev lactation)-->T
        C(CM in prev lact)-->T
        A-->U
        P-->U
        M-->U
        S-->U
        C-->U
        C-->M
        P-->C
        P-->S
        P-->M
        A-->P
        A-->C
        A-->S
        A-->M
        M-->S
        C-->S
        style A fill:#FFFFFF, stroke-width:0px
        style T fill:#FFFFFF, stroke-width:2px
        style P fill:#FFFFFF, stroke-width:0px
        style M fill:#FFFFFF, stroke-width:0px
        style S fill:#FFFFFF, stroke-width:0px
        style C fill:#FFFFFF, stroke-width:0px
        style I fill:#FFFFFF, stroke-width:0px
        style U fill:#FFFFFF, stroke-width:2px
        ")
```
According to this DAG, I may need to control for the following variables:

Parity ["Parity"].  Will not offer Age ["Age"] as it is highly correlated.

Yield at most recent test before dry off ["DOMY"]

Somatic cell count at last herd test during previous lactation ["DOSCC"] <- will not offer PrevSCCHI as it was correlated with DOSCC

Clinical mastitis in previous lactation ["PrevCM"]

<br>
<br>
<br>
<br>

### Step 3: Create model with all potential confounders

Cows that did not calve are excluded (left censored)

Reason for R censor = 120 DIM

```{r}
library(broom)
library(survival)
coxph(Surv(Cull2TAR, Cull2) ~ Parity + DOMY + DOSCC + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
```
<br>
<br>
<br>
<br>

### Step 4: Investigate if covariates meet proportional hazards assumption
Both DOSCC and DOMY don't meet the assumption of proportional hazards


```{r}
SR <- cox.zph(coxph(Surv(Cull2TAR, Cull2) ~ Parity + DOMY + DOSCC + PrevCM + Tx + cluster(FARMID), data=SDCTCOW))
SR
```



Schoenfield residual plots
```{r fig.height=8}
ggcoxzph(SR,var = c("TxCulture","TxAlgorithm"))
```
<br>
<br>
<br>
<br>
DOSCC and DOMY don't meet the assumption of proportional hazards
```{r fig.height=8}
ggcoxzph(SR,var = c("DOSCC", "DOMY"))
```
```{r fig.height=8}
ggcoxzph(SR,var = c("Parity2","Parity3"))
```
```{r fig.height=8}
ggcoxzph(SR,var = c("PrevCM1"))
```
<br>
<br>
<br>
<br>

Refit cox model with seperate baselines (stratified) for DOMY and DOSCC.

No evidence of other time-varying covariates or predictors (Tx).  
```{r}
SR <- coxph(Surv(Cull2TAR, Cull2) ~ Parity + strata(DOMYcat) + strata(DOSCM) + PrevCM + Tx + cluster(FARMID), data=SDCTCOW)
SR <- cox.zph(SR)
SR
```
<br>
<br>
<br>
<br>

### Step 5: Assess for effect measure modification

Tx : FARMID - could not assess this using Cox regression as model did not converge or reported unusually large SEs for some interaction terms. 

```{r}
SR <- coxph(Surv(Cull2TAR, Cull2) ~ Tx*FARMID + Parity + PrevCM + Parity + strata(DOMYcat) + strata(DOSCM), data=SDCTCOW)
tidy(SR)
```
<br>
<br>
<br>
<br>
I will assess effect Tx:farm interaction using logistic regression: 

Wald test for interaction term was P > 0.05. 
```{r}
mm0 <- glm(CM ~ Tx*FARMID + Parity + PrevCM + Parity + DOMYcat + DOSCM, data=SDCTCOW)
car::Anova(mm0)
```
<br>
<br>
<br>
<br>
Assess for other interactions using Wald testfrom Cox regression. 

Wald test was P > 0.05 for Tx:PrevCM interaction
. 
```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx*PrevCM + Parity + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW)
summary(mm0)
wald.test(b = coef(mm0), Sigma = vcov(mm0), Terms = 6:7)
```
<br>
<br>
<br>
<br>
Wald test was P < 0.05 for Tx:Parity interaction
. 
```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx*Parity + PrevCM + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW)
summary(mm0)
wald.test(b = coef(mm0), Sigma = vcov(mm0), Terms = 6:9)
```
<br> 
<br>
<br>
Investigate potential effect measure modification by doing stratified models

Parity = 1
Frequency table
```{r}
table(SDCTCOW$Tx[SDCTCOW$Parity==1],SDCTCOW$Cull2[SDCTCOW$Parity==1])
```
<br>
<br>
<br>

#### Model (Parity = 1)
```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW[SDCTCOW$Parity==1,]) %>% tidy()
mm0$HR <- exp(mm0$estimate)
mm0$LCL <- exp(mm0$conf.low)
mm0$UCL <- exp(mm0$conf.high)
mm0 %>% select("term","HR","LCL","UCL")
```

<br>
<br>
<br>

#### Parity = 2

Frequency table
```{r}
table(SDCTCOW$Tx[SDCTCOW$Parity==2],SDCTCOW$Cull2[SDCTCOW$Parity==2])
```

```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW[SDCTCOW$Parity==2,]) %>% tidy()
mm0$HR <- exp(mm0$estimate)
mm0$LCL <- exp(mm0$conf.low)
mm0$UCL <- exp(mm0$conf.high)
mm0 %>% select("term","HR","LCL","UCL")
```

<br>
<br>
<br>

#### Parity = 3 or greater
Frequency table
```{r}
table(SDCTCOW$Tx[SDCTCOW$Parity==3],SDCTCOW$Cull2[SDCTCOW$Parity==3])
```

```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW[SDCTCOW$Parity==3,]) %>% tidy
mm0$HR <- exp(mm0$estimate)
mm0$LCL <- exp(mm0$conf.low)
mm0$UCL <- exp(mm0$conf.high)
mm0 %>% select("term","HR","LCL","UCL")
```

This finding suggests that potential culling risks associated with SDCT may be higher in parity 1 cows than in multiparous animals.  However these HR estimates in all 3 parity groups are imprecise (wide confidence intervals) because of a small number of culling/death events.  For example, in lactation 1 animals: 6 in BDCT, 11 in Algorithm and 12 in Culture. Therefore, this difference in effects across levels of parity may be due to chance alone, and not worth investigating too closely. 

Decision: Report main effects.

<br>
<br>
<br>

### Step 6: Remove unnecessary covariates (backwards selection using 10% rule)

The order for removing covariates will be in increasing likelihood of being a confounder, which is based on my knowledge about the variables and their distribution in treatment groups.

This order will be: DOMYcat, DOSCM, PrevCM, Parity

Step 6a: Full model
```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + Parity + strata(DOMYcat) + strata(DOSCM) + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
<br>
<br>
<br>
<br>
Step 6b: removing DOMYcat
```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + Parity + strata(DOSCM) + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
HR for culture and algorithm didn't change by >10%.  DOMYcat stays out. 
<br>
<br>
<br>
<br>

Step 6c: removing DOSCM
```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + PrevCM + Parity + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
HR changed by <10%.  DOSCM stays out. 
<br>
<br>
<br>
<br>

Step 6d: removing PrevCM
```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + Parity + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
HR changed by <10%.  Leave PrevCM out. 
<br>
<br>
<br>
<br>
Step 6e: removing Parity
```{r}
mm0 <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + cluster(FARMID), data=SDCTCOW) %>% tidy() %>% select("term","estimate")
mm0$HR <- exp(mm0$estimate)
mm0
```
HR changed by <10%. Parity stays out.

<br>
<br>
<br>
<br>

### Step 7a: Final cox model for culling or death (1 - 120 DIM)
No covariates included, as no evidence for confounding.
```{r}
CoxCull <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + cluster(FARMID), data=SDCTCOW) %>% tidy()
CoxCull$HR <- exp(CoxCull$estimate)
CoxCull$LCL <- exp(CoxCull$conf.low)
CoxCull$UCL <- exp(CoxCull$conf.high)
CoxCull <- CoxCull %>% select(term,HR,LCL,UCL,robust.se,p.value)
CoxCull
```


#### Check schoenfield residuals for final model
```{r fig.height=8}
SR <- coxph(Surv(Cull2TAR, Cull2) ~ Tx + cluster(FARMID), data=SDCTCOW)
cox.zph(SR)
SR <- cox.zph(SR)
ggcoxzph(SR,var = c("TxCulture","TxAlgorithm"))
```


### Step 7b: Final cox model for culling or death (1 - 120 DIM) using P-value based backwards stepwise selection
```{r}
CoxCull <- coxph(Surv(CullTAR, Cull2) ~ Tx + Parity + DOSCC + PrevCM + cluster(FARMID), data=SDCTCOW) %>% tidy()
CoxCull$HR <- exp(CoxCull$estimate)
CoxCull$LCL <- exp(CoxCull$conf.low)
CoxCull$UCL <- exp(CoxCull$conf.high)
CoxCull <- CoxCull %>% select(term,HR,LCL,UCL,robust.se,p.value)
CoxCull
```
Estimates are similar to 10% rule based approach
<br>
<br>
<br>
<br>





# Changing datasets: DHI dataset with multiple rows per cow

Dataset example
```{r}
SDCTCOWDHI$Tx <- 
  factor(SDCTCOWDHI$Tx, 
         levels=c(0,1,2),
         labels=c("Blanket",
                  "Culture", 
                  "Algorithm"))

DHIcheck <- SDCTCOWDHI %>% select(Tx,CowID,FARMID,DIM,TestDIMcat20,LSCC,MY,Parity,PrevCM,DOMY,DOSCC)
head(DHIcheck, n=10)
```
<br>
<br>
<br>
<br>

# Inspect data
```{r}
DHIoutcome <- SDCTCOWDHI %>% select(SCC,MY,SCM)
DHIoutcome$logSCC <- log(DHIoutcome$SCC + 1)
#summarytools::dfSummary(DHIoutcome, style='grid')
print(summarytools::dfSummary(DHIoutcome, valid.col=FALSE, graph.magnif=0.8, style="grid"), method = "render")

```
Very little missing data. Will do complete case analysis.
<br>
<br>
<br>
<br>

## Assessing normality for continuous outcome variables

Somatic cell count (log x 10,000 cells)
```{r}
qqPlot(log(SDCTCOWDHI$SCC+1))
```

```{r}
hist(log(SDCTCOWDHI$SCC+1))
```
<br>
<br>
<br>
<br>
Milk yield (kg)
```{r}
qqPlot(SDCTCOWDHI$MY)
```
```{r}
hist(SDCTCOWDHI$MY)
```
<br>
<br>
<br>
<br>

# Outcome 3: Somatic cell count

## Modelling plan
Model type: Linear mixed models, random intercepts for farm and cow will be fitted to account for repeated measures within cows, and clustering of cows within herds

Step 1: Identify potential confouders using a directed acyclic graph (DAG)

Step 2: Identify correlated variables using pearson and kendalls correlation coefficients

Step 3: Create model with all potential confounders

Step 4: Investigate potential effect measure modification

Step 5: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if estimated difference in SCC changes by >10% after removing the covariate, the covariate is retained in the model)

Step 6: Report final model

Step 7: Model diagnostics

### Step 1 & 2 Identify potential confounders using a DAG
```{r fig.width=10}
library(DiagrammeR)
mermaid("graph LR
        T(Treatment)-->U(SCC)
        A(Age)-->T
        P(Parity)-->T
        M(Yield at dry-off)-->T
        S(SCC during prev lactation)-->T
        C(CM in prev lact)-->T
        D(Days in milk at test)-->U
        D-->T
        A-->U
        P-->U
        M-->U
        S-->U
        C-->U
        C-->M
        P-->C
        P-->S
        P-->M
        A-->P
        A-->C
        A-->S
        A-->M
        M-->S
        C-->S
        style A fill:#FFFFFF, stroke-width:0px
        style T fill:#FFFFFF, stroke-width:2px
        style P fill:#FFFFFF, stroke-width:0px
        style M fill:#FFFFFF, stroke-width:0px
        style S fill:#FFFFFF, stroke-width:0px
        style C fill:#FFFFFF, stroke-width:0px
        style I fill:#FFFFFF, stroke-width:0px
        style D fill:#FFFFFF, stroke-width:0px
        style U fill:#FFFFFF, stroke-width:2px
        ")
```
According to this DAG, I may need to control for the following variables:

Parity ["Parity"] <- Age not offered as highly correlated

Yield at most recent test before dry off ["DOMY"]

Somatic cell count at last herd test during previous lactation ["DOSCC"] <- PrevSCCHI not offered as correlated

Clinical mastitis in previous lactation ["PrevCM"]

Days in milk at herd test (category, 0-20 "10", 21-40 "30" etc) ["TestDIMcat20"]



<br>
<br>
<br>
<br>

### Step 3: Create model with all potential confounders
```{r}
mm0 <- lmer(LSCC ~ Tx + TestDIMcat20 + Parity + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
summary(mm0)
car::vif(mm0)
```
<br>
<br>
<br>
<br>

### Step 4: Investigate effect measure modification

Tx:FARM (P > 0.05)
```{r}
mm0 <- lmer(LSCC ~ Tx*FARMID + Parity + TestDIMcat20 + DOSCC + DOMY + PrevCM + (1|CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```
<br>
<br>
<br>
<br>

Tx:DIM category at herd test (P > 0.05)
```{r}
mm0 <- lmer(LSCC ~ Tx*TestDIMcat20 + Parity + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```
<br>
<br>
<br>
<br>
Tx:Parity (P > 0.05)
```{r}
mm0 <- lmer(LSCC ~ Tx*Parity + TestDIMcat20 + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```
<br>
<br>
<br>
<br>
Tx:PrevCM (P > 0.05)
```{r}
mm0 <- lmer(LSCC ~ Tx*PrevCM + Parity + TestDIMcat20 + DOSCC + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```
<br>
<br>
<br>
<br>
Tx:DOMY (P > 0.05)
```{r}
mm0 <- lmer(LSCC ~ Tx*DOMY + PrevCM + Parity + TestDIMcat20 + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```

### Step 5: Remove unneccesary covariates in backwards stepwise fashion using 10% rule

The order for removing covariates will be in increasing likelihood of being a confounder, which is based on my knowledge about the variables and their distribution in treatment groups.

This order will be: DOMY, Parity, PrevCM, DOSCC

TestDIMcat20 will not be removed.

Step 5a: Full model
```{r}
mm0 <- lmer(LSCC ~ Tx + PrevCM + Parity + TestDIMcat20 + DOSCC + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
mm0 %>% tidy()
```
<br>
<br>
<br>
<br>
Step 5b: removing DOMY
```{r}
mm0 <- lmer(LSCC ~ Tx + PrevCM + Parity + TestDIMcat20 + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0%>% tidy()
```
Changed by <10%.  DOMY stays out. 
<br>
<br>
<br>
<br>
Step 5b: removing Parity
```{r}
mm0 <- lmer(LSCC ~ Tx + PrevCM + TestDIMcat20 + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI)
mm0 %>% tidy()
```
Changed by <10%. Parity stays out. 

<br>
<br>
<br>
<br>
Step 5c: removing PrevCM
```{r}
mm0 <- lmer(LSCC ~ Tx + TestDIMcat20 + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy()
```
Changed by >10%. PrevCM stays in. 
<br>
<br>
<br>
<br>
Step 5d: removing DOSCC
```{r}
mm0 <- lmer(LSCC ~ Tx + PrevCM + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
mm0 %>% tidy()
```
Changed by > 10%.  DOSCC stays in. 
<br>
<br>
<br>
<br>

### Step 6a: Final model for SCC (1 - 120 DIM)
```{r}
mm0 <- lmer(LSCC ~ Tx + PrevCM + DOSCC + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
mm0 %>% tidy(conf.int=TRUE)
```

#### ICC for SCC (1 - 120 DIM)
```{r}
mm0 <- lmer(LSCC ~ 1 + (1|FARMID/CowID), data=SDCTCOWDHI)
summary(mm0)
```

ICC (CowID) = 0.35
ICC (FARMID) = 0.02

Most clustering is happening within cow, which is not a suprise given this is longitudinal data. 

### Step 6b: Final model for SCC (1 - 120 DIM) using P-value based backwards selection
```{r}
lmer(LSCC ~ Tx + Parity + PrevCM + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI) %>% summary()

lmer(LSCC ~ Tx + Parity + PrevCM + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI) %>% car::Anova() %>% tidy()

```
Estimates are very similar to 10% rule based approach.
<br>
<br>
<br>
<br>

### Step 6c: Final model (using 10% rule) reported as estimated marginal means (~LSmeans)
Mean log SCC
```{r}
mm0 <- lmer(LSCC ~ Tx + PrevCM + DOSCC + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
emm <- emmeans(mm0, ~Tx) %>% tidy()
emm
```


### Step 6c: Final model (using 10% rule) reported as back-transformed estimated marginal means (~LSmeans)
Geometric mean SCC
```{r}
mm0 <- lmer(LSCC ~ Tx + PrevCM + DOSCC + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
emm <- emmeans(mm0, ~Tx) %>% tidy()
emm$SCC <- exp(emm$estimate) 
emm$LCL <- exp(emm$asymp.LCL)
emm$UCL <- exp(emm$asymp.UCL)
emm <- emm %>% select(Tx,SCC,LCL,UCL)
emm
```
<br>
<br>
<br>


Reported as back-transformed estimated marginal means by herd test day, no interaction with test DIM
```{r}
mm0 <- lmer(LSCC ~ Tx + TestDIMcat20 + DOSCC + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
atx <- c(10,30,50,70,90,110)
emm <- emmeans(mm0, ~Tx*TestDIMcat20, at=list(atx)) %>% tidy()
emm$SCC <- exp(emm$estimate)
emm$LCL <- exp(emm$asymp.LCL)
emm$UCL <- exp(emm$asymp.UCL)
emm <- emm %>% select(Tx,TestDIMcat20,SCC,LCL,UCL)
curve <- ggplot(emm) + coord_cartesian(ylim = (c(0,100))) + aes(x=TestDIMcat20, y=SCC, group=Tx, colour=Tx) + geom_point() + geom_line(aes(colour=Tx,linetype=Tx)) + geom_ribbon(aes(ymin=emm$LCL, ymax=emm$UCL,colour=Tx,fill=Tx), linetype=0, alpha=0.1)
curve
```
<br>
<br>
<br>
<br>

Reported as back-transformed estimated marginal means by herd test day, with interaction with test DIM
```{r}
mm0 <- lmer(LSCC ~ Tx*TestDIMcat20 + PrevCM + DOSCC + (1|FARMID/CowID), data=SDCTCOWDHI)
atx <- c(10,30,50,70,90,110)
emm <- emmeans(mm0, ~Tx*TestDIMcat20, at=list(atx)) %>% tidy()
emm$SCC <- exp(emm$estimate)
emm$LCL <- exp(emm$asymp.LCL)
emm$UCL <- exp(emm$asymp.UCL)
emm <- emm %>% select(Tx,TestDIMcat20,SCC,LCL,UCL)
curve <- ggplot(emm) + coord_cartesian(ylim = (c(0,100))) + aes(x=TestDIMcat20, y=SCC, group=Tx, colour=Tx) + geom_point() + geom_line(aes(colour=Tx,linetype=Tx)) + geom_ribbon(aes(ymin=emm$LCL, ymax=emm$UCL,colour=Tx,fill=Tx), linetype=0, alpha=0.1)
curve
```
<br>
<br>
<br>
<br>

### Step 7: Model diagnostics
Checking homoskedasticity assumption (variance of residuals)
```{r}
mm0 <- lmer(LSCC ~ Tx + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI)
ggplot(data.frame(eta=predict(mm0,type="link"),pearson=residuals(mm0,type="pearson")),
       aes(x=eta,y=pearson)) +
  geom_point() +
  theme_bw()
```


Checking normality of residuals
```{r}
qqnorm(residuals(mm0))
```
Evidence of small L tail. Although some evidence of heteroskedasticity and not perfectly normal residuals, I believe these are allowable for this model. 


# Outcome 4: Milk yield


## Modelling plan
Model type: Linear mixed models, random intercepts for farm and cow will be fitted to account for repeated measures within cows, and clustering of cows within herds

Step 1: Identify potential confouders using a directed acyclic graph (DAG)

Step 2: Identify correlated variables using pearson and kendalls correlation coefficients

Step 3: Create model with all potential confounders

Step 4: Investigate potential effect measure modification

Step 5: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if estimated difference in milk yield changes by >10% after removing the covariate, the covariate is retained in the model)

Step 6: Report final model

Step 7: Model diagnostics

### Step 1 & 2 Identify potential confounders using a DAG
```{r fig.width=10}
library(DiagrammeR)
mermaid("graph LR
        T(Treatment)-->U(Milk yield)
        A(Age)-->T
        P(Parity)-->T
        M(Yield at dry-off)-->T
        S(SCC during prev lactation)-->T
        C(CM in prev lact)-->T
        D(Days in milk at test)-->U
        D-->T
        A-->U
        P-->U
        M-->U
        S-->U
        C-->U
        C-->M
        P-->C
        P-->S
        P-->M
        A-->P
        A-->C
        A-->S
        A-->M
        M-->S
        C-->S
        style A fill:#FFFFFF, stroke-width:0px
        style T fill:#FFFFFF, stroke-width:2px
        style P fill:#FFFFFF, stroke-width:0px
        style M fill:#FFFFFF, stroke-width:0px
        style S fill:#FFFFFF, stroke-width:0px
        style C fill:#FFFFFF, stroke-width:0px
        style I fill:#FFFFFF, stroke-width:0px
        style D fill:#FFFFFF, stroke-width:0px
        style U fill:#FFFFFF, stroke-width:2px
        ")
```
According to this DAG, I may need to control for the following variables:

Parity ["Parity"] <- Age not offered as highly correlated

Yield at most recent test before dry off ["DOMY"]

Somatic cell count at last herd test during previous lactation ["DOSCC"] <- PrevSCCHI not offered as correlated

Clinical mastitis in previous lactation ["PrevCM"]

Days in milk at herd test (category, 0-20 "10", 21-40 "30" etc) ["TestDIMcat20"]

<br>
<br>
<br>
<br>

### Step 3: Create a model with all potential covariates

```{r}
mm0 <- lmer(MY ~ Tx + TestDIMcat20 + Parity + DOSCC + PrevCM + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
summary(mm0)
car::vif(mm0)
```
<br>
<br>
<br>
<br>

### Step 4: Investigate effect measure modification

### Tx:FARM (P < 0.05)
```{r}
mm0 <- lmer(MY ~ Tx*FARMID + Parity + TestDIMcat20 + DOSCC + DOMY + PrevCM + (1|CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```

Significant interaction term.

Descision: Revisit this after covariates are finalized.
<br>
<br>
<br>
<br>
Tx:DIM category at herd test (P > 0.05)
```{r}
mm0 <- lmer(MY ~ Tx*TestDIMcat20 + Parity + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```
<br>
<br>
<br>
<br>
Tx:Parity (P > 0.05)
```{r}
mm0 <- lmer(MY ~ Tx*Parity + TestDIMcat20 + DOSCC + DOMY + PrevCM + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```
<br>
<br>
<br>
<br>
Tx:PrevCM (P > 0.05)
```{r}
mm0 <- lmer(MY ~ Tx*PrevCM + Parity + TestDIMcat20 + DOSCC + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```
<br>
<br>
<br>
<br>

### Step 5: Remove unnecessary covariates using backwards selection (10% rule)

The order for removing covariates will be in increasing likelihood of being a confounder, which is based on my knowledge about the variables and their distribution in treatment groups.

This order will be: DOSCC, PrevCM, Parity, DOMY

TestDIMcat20 will not be removed (forced into model). 

 


Step 5a: Full model
```{r}
mm0 <- lmer(MY ~ Tx + PrevCM + Parity + TestDIMcat20 + DOSCC + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy() %>% select(term,estimate)
```
<br>
<br>
<br>
<br>
Step 5b: Removing DOSCC
```{r}
mm0 <- lmer(MY ~ Tx + PrevCM + Parity + TestDIMcat20 + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy() %>% select(term,estimate)
```
Changed by <10%. DOSCC stays out
<br>
<br>
<br>
<br>

Step 5c: removing PrevCM
```{r}
mm0 <- lmer(MY ~ Tx + Parity + TestDIMcat20 + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)  
mm0 %>% tidy() %>% select(term,estimate)
```
Changed by < 10%. PrevCM stays out. 

<br>
<br>
<br>
<br>
Step 5d: removing Parity
```{r}
mm0 <- lmer(MY ~ Tx + TestDIMcat20 + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy() %>% select(term,estimate)
```
Changed by >10%.  Parity stays in.
<br>
<br>
<br>

Step 5e: removing DOMY
```{r}
mm0 <- lmer(MY ~ Tx + Parity + TestDIMcat20 + (1|FARMID/CowID), data=SDCTCOWDHI) 
mm0 %>% tidy() %>% select(term,estimate)
```
Changed by >10%.  DOMY stays in. 
<br>
<br>
<br>
<br>

### Revisit effect measure modification previously identified
Effect measure modification with herd (P < 0.05)
```{r}
mm0 <- lmer(MY ~ Tx*FARMID + TestDIMcat20 + Parity + DOMY + (1|CowID), data=SDCTCOWDHI)
car::Anova(mm0)
```

Decision - will investigate effect estimates stratified by herd
<br>
<br>
<br>
<br>

### Step 6a: Final model for milk yield (1 - 120 DIM), stratified by herd. 
Model output
```{r}
mm0 <- lmer(MY ~ Tx*FARMID + TestDIMcat20 + Parity + DOMY + (1|CowID), data=SDCTCOWDHI)
emmeans(mm0,pairwise ~ Tx | FARMID)
```
It appears that herd 2 (87 cows) and herd 6 (42 cows) have extreme results compared with the other herds.  In herd 2, BDCT had much higher MY than SDCT cows.  In herd 6, it was the opposite effect.  Given these were the smallest herds in the study, I will report a pooled result. 
<br>
<br>
<br>
<br>

### Step 6bi: Final model reported without herd interaction
Model output
```{r}
summary(lmer(MY ~ Tx + TestDIMcat20 + Parity + DOMY+ (1|FARMID/CowID), data=SDCTCOWDHI))
```

Model output (tidy)
```{r}
lmer(MY ~ Tx + TestDIMcat20 + Parity + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI) %>% tidy(conf.int=TRUE)
```

#### ICC for MY (1 - 120 DIM)
```{r}
mm0 <- lmer(MY ~ 1 + (1|FARMID/CowID), data=SDCTCOWDHI)
summary(mm0)
```

ICC (CowID) = 0.25
ICC (FARMID) = 0.09


Emmeans without TestDIM interaction
```{r}
mm0 <- lmer(MY ~ Tx + TestDIMcat20 + Parity + DOMY+ (1|FARMID/CowID), data=SDCTCOWDHI)

emmeans(mm0,~Tx) %>% tidy
```


### Step 6bii: Final model reported without herd interaction (using P-value based backwards elimination)
Model output
```{r}
summary(lmer(MY ~ Tx + TestDIMcat20 + Parity + (1|FARMID/CowID), data=SDCTCOWDHI))
```


<br>
<br>
<br>
<br>

### Step 6biii: Final model (using 10% rule) reported as estimated marginal means by test DIM category (no interaction with test DIM)
```{r}
mm0 <- lmer(MY ~ Tx + TestDIMcat20 + Parity + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)

atx <- c(10,30,50,70,90,110)
emm <- emmeans(mm0, ~Tx*TestDIMcat20) %>% tidy()
emm$MY <- emm$estimate
emm$LCL <- emm$asymp.LCL
emm$UCL <- emm$asymp.UCL
emm %>% select(Tx,TestDIMcat20,MY,LCL,UCL)
```

Plotting model as predicted values
```{r}
curve <- ggplot(emm) + coord_cartesian(ylim = (c(0,55))) + aes(x=TestDIMcat20, y=MY, group=Tx, colour=Tx) + geom_point() + geom_line(aes(colour=Tx,linetype=Tx)) + geom_ribbon(aes(ymin=emm$LCL, ymax=emm$UCL,colour=Tx,fill=Tx), linetype=0, alpha=0.1)
curve
```
<br>
<br>
<br>
<br>
Reported as estimated marginal means by test day category with interaction with herd test DIM
```{r}
mm0 <- lmer(MY ~ Tx*TestDIMcat20 + Parity + DOMY + (1|FARMID/CowID), data=SDCTCOWDHI)
atx <- c(10,30,50,70,90,110)
emm <- emmeans(mm0, ~Tx*TestDIMcat20, at=list(atx)) %>% tidy()
emm$MY <- emm$estimate
emm$LCL <- emm$asymp.LCL
emm$UCL <- emm$asymp.UCL
emm <- emm %>% select(Tx,TestDIMcat20,MY,LCL,UCL)

curve <- ggplot(emm) + coord_cartesian(ylim = (c(0,55))) + aes(x=TestDIMcat20, y=MY, group=Tx, colour=Tx) + geom_point() + geom_line(aes(colour=Tx,linetype=Tx)) + geom_ribbon(aes(ymin=emm$LCL, ymax=emm$UCL,colour=Tx,fill=Tx), linetype=0, alpha=0.1)
curve
```

### Step 7: Model diagnostics
Checking homoskedasticity assumption (variance of residuals)
```{r}
mm0 <- lmer(MY ~ Tx + TestDIMcat20 + Parity +DOMY+ (1|FARMID/CowID), data=SDCTCOWDHI)
ggplot(data.frame(eta=predict(mm0,type="link"),pearson=residuals(mm0,type="pearson")),
       aes(x=eta,y=pearson)) +
  geom_point() +
  theme_bw()
```

Checking normality of residuals
```{r}
qqnorm(residuals(mm0))
```

I am happy with homoskedasticity and normal residuals assumptions

